ECON 341 HW 3
A local charity has decided to solicit donations door-to-door. The table below shows estimated donations for each hour a volunteer spends in the city, in the suburbs, and on campus.
$ 628.
Given the above information, and given an optimizing solution, the fourth hour solicited yielded
$ 64 in additional donations.
A Blue Ribbon Committee has decided that acid rain should be reduced and is trying to determine the optimal level of reduction. There are benefits from reducing acid rain (more wildlife and forests, better health, etc.), but there are also costs. The committee estimates that the marginal benefit of each unit of reduction is $700 - 5R, where R is units of reduction, and the marginal cost is 2R. If the committee wants to maximize the net benefit from reducing acid rain, what is the optimal level of pollution reduction?
$100
Based on the above information, if operators receive $400 a week, what is the lowest possible total cost of personal calls?
$1450
A housecleaning company receives $25 for each house cleaned. The table below gives the relation between the number of workers and the number of houses that can be cleaned per week.
$150.
Given the above information, what is Dr. X's maximum possible raise if she works 50 hours?
$1600
Based on the above info, if the company want to maximize profit and hires three workers, the wage rate of a housecleaner can be no more than
$175.
A Blue Ribbon Committee has decided that acid rain should be reduced and is trying to determine the optimal level of reduction. There are benefits from reducing acid rain (more wildlife and forests, better health, etc.), but there are also costs. The committee estimates that the marginal benefit of each unit of reduction is $1,400 - 5R, where R is units of reduction, and the marginal cost is 2R. If the committee wants to maximize the net benefit from reducing acid rain, what is marginal cost at the optimal level of reduction?
$200
Based on the above info, if the wage rate of a housecleaner is $130, what is the maximum amount of profit the company can earn?
$230
A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while the last nurse hired treated 1,000 extra patients in a year. If doctors make $40,000 a year, what do nurses make?
$25,000 a year
An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls).Based on the above information, if operators receive $25 an hour, what is the minimum possible total cost of personal calls (per hour)?
$255
Given the above info, if the cost of a stolen radio is $25, what is the MOST the firm would be willing to pay to hire the first security guard?
$500
Your firm sells club soda in both grocery stores and convenience stores. You have a budget of $550 for store displays, and must decide how to allocate this budget between grocery stores and convenience stores to maximize the total number of sales. The following table shows the total number of units that can be sold in grocery stores and convenience stores, according to the number of displays in each type of store. Displays in grocery stores cost $150 each and displays in convenience stores cost $100 each.
1 grocery store display and 4 convenience store displays
Given the above information, and given a budget of $550, the maximum possible number of sales is
1,960.
Use the following marginal benefit and marginal cost functions for activity A: MB = 100 - 5A MC = 20 + 3A The optimal level of A is
10
What is marginal benefit for the 3rd unit of the activity?
175
Based on the information above, how many EXTRA votes will the politician receive if he devotes one more hour to speaking engagements (i.e., speaks 10 instead of 9 hours per week)?
180
An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls).Based on the above information, if operators receive $25 an hour, how many operators should the agency hire?
2
Based on the information above, how many air scrubbers should the plant install in order to minimize the total cost of pollution?
2
Given the above info, if each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?
2
Dr. X, an assistant professor at a large state university, is trying to decide how to allocate the 50 hours a week she spends working among the various activities expected of an assistant professor. The professor wants to maximize her raise next year and the table shows estimates of how time spent in each activity will contribute to her raise:Given the above information, how should she allocate her time?
20 hours research, 15 hours teaching, 15 hours service
Given the above information, if she decides that she will work 54 hours a week instead, how should she allocate her time?
20 hours research, 18 hours teaching, 16 hours service
Based on the above information, if operators receive $300 a week, how many operators should the agency hire?
3
Given the above information, if each inspector is paid $100 a day, how many inspectors should the firm hire to minimize the total cost of defective toys?
3
What is the net benefit of the 5th unit of the activity? (bottom line 500)
3
Based on the above information, how should the student allocate her time?
3 hours economics, 4 hours statistics, 2 hours finance
Given the above information, at the optimal choice with a budget of $550, the last dollar spent on grocery store displays yields
3.3 additional sales.
A dentist's office, which wants to serve the maximum number of patients given a fixed payroll, currently has two dentists and four dental hygienists. Dentists earn $60,000 a year and hygienists earn $15,000 a year. If the office is hiring the optimal combination of dentists and hygienists, and the last dentist hired served 120 additional patients, how many patients will the last hygienist hired add?
30
Given the above info, if each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?
4
The optimal level of activity is: (bottom line 825)
4
Given the above information, if the cost of each defective toy rises to $50, while inspectors are paid $150 a day, how many inspectors should the firm hire?
5
A politician, who wants to receive the maximum number of votes, spends 9 hours a week speaking to various groups. The table below shows his estimates of how time spent with each group will affect the number of votes he receives: Based on the information above, how should the politician allocate his speaking time?
5 hours to LPM, 1 hours to TM, 3 hours to LCL
What is the net benefit of the 6th unit of the activity?
50
Given the above information, at the optimal choice, the last dollar spent on hiring waiters yielded
6 additional meals.
A local charity has decided to solicit donations door-to-door. The table below shows estimated donations for each hour a volunteer spends in the city, in the suburbs, and on campus.
6 hours in the city, 4 hours in the suburbs, 0 hours on campus
What is marginal benefit for the 4th unit of the activity?
65
Randolph is taking three courses this semester: economics, statistics, and finance. He has decided to spend 20 hours per week studying (in addition to attending all his classes) and his objective is to maximize his average grade, which means maximizing the total of his grades in the three courses. The table shows Randolph's estimate of the relation between time spend studying and his grade for each course. Based on the above info, how should Randolph allocate his time?
7 hours economics, 7 hours statistics, 6 hours finance
What is the net benefit of the 5th unit of the activity?
70
Based on the above information, what is the maximum AVERAGE grade the student can earn if she studies 9 hours per week?
78.3
Based on the above info, what is the maximum AVERAGE grade Randolph can earn if he studies 20 hours per week?
81.7
Given the above information, and given the fixed payroll, the maximum number of meals that can be served is
850.
Given the above information, what is the maximum possible number of customers that can be served with a payroll of $32?
936
Based on the above information, how should the manager with an annual budget of $160,000, allocate this budget in order to maximize the number of new products developed?
Hire 3 engineers and 2 market researchers.
Given the above info, if the manager has a payroll of $80,000, how should the budget be allocated in order to maximize the number of customers served?
Hire four HS and two B.
Based on the above information, how should a manager with an annual budget of $240,000, allocate this budget in order to maximize the number of new products developed?
Hire four engineers and four market researchers.
Given the above info, if the manager's payroll is $120,000, what should be done to maximize the number of customers served?
Hire six HS and three B.
Based on the above information, how should a manager with an annual budget of $140,000, allocate this budget in order to maximize the number of new products developed?
Hire three engineers and one market researcher
A grocery store hires cashiers and baggers. Cashiers earn $8 an hour; baggers earn $4 an hour. The manager, who wants to maximize the number of customers served given a fixed payroll, expects the following productivity from cashiers and baggers: Given the above information, with a payroll of $32 (per hour), how should the manager allocate this budget?
Hire two cashiers and four baggers
Given the above information, if the manager has an annual budget of $120,000, how should this budget be allocated in order to maximize the number of new products developed?
Hire two engineers and three market researchers.
A firm is deciding whether or not to close down its plant and modernize by installing new technology. Which of the following should management ignore when making the decision?
How much the present plant cost
Given the above info, if the manager currently has three HS and three B, what must be true?
More customers could be served if the manager hires more HS and fewer B.
Given the above information, if the manager currently has two engineers and one market researcher, what must be true?
More new products will be developed if he hires fewer engineers and more market researchers.
Based on the above information, if the manager currently hires four engineers and one market researcher, what must be true?
More new products would be developed if she hires fewer engineers and more market researchers.
A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while the last nurse hired treated 1,000 extra patients in a year. If doctors make $50,000 a year and nurses make $40,000 a year, then
a and d
For a constrained minimization problem, the decision maker
all of the above
When the choice variable is a continuous variable, the decision rule for an unconstrained maximization problem is:
all of the above
Which of the following statements represents bad decision making?
all of the above
If profits depend on both how much is produced (output) and on the level of advertising, then a profit-maximizing firm should choose the levels of output and advertising at which
both a and b
The optimal level of pollution reduction is that level at which
both a and d
A firm will maximize profit by producing that level of output at which
both b and c
A package delivery service uses vans and employees to deliver the maximum number of packages given a fixed budget. The last van added 600 packages to total output, while the last employee added 500 packages. If vans cost $400 per week and employees earn $300 per week, the firm
both b and c
Gigi consumes only Perrier and cheese. In order to maximize her happiness subject to limited income, Gigi should purchase the amounts of Perrier and cheese at which
both b and c
A package delivery service currently has 12 vans and 16 employees. Vans cost $400 per week and employees earn $300 per week. The last van added 480 packages delivered to total output, while the last employee added 450 packages. The firm
both c and d
A clinic uses doctors and nurses to serve the maximum number of patients given a limited annual payroll. The clinic currently has 10 doctors and 30 nurses. The last doctor hired can serve 300 additional patients, while the last nurse hired can serve 200 additional patients. If doctors make $60,000 a year and nurses make $20,000 a year, the clinic
could serve more patients with the same payroll by hiring more nurses and fewer doctors.
In order to minimize the NET costs associated with crime,
crime should be reduced to the level at which the marginal cost from crime equals the marginal cost of crime prevention.
A metal refining plant emits sulfur dioxide into the air and has decided to install air scrubbers to reduce the amount of pollution. Each scrubber costs $180,000 and the Environmental Protection Agency (EPA) fines the plant $5,000 for every part of pollution emitted per million. Based on the information above, the first air scrubber __________ (increases/decreases) the total cost of pollution by $______.
decreases, $ 70,000
Choice variables
determine the value of the objective function
Use the following marginal benefit and marginal cost functions for activity A: MB = 100 - 5A MC = 20 + 3A The fifth unit of activity A will
increase net benefits by 40.
In making a decision about whether to increase its advertising budget the firm management should not consider
interest payments on the firm's loan.
The optimization rule for unconstrained optimization is to select that level of activity at which
marginal benefit equals marginal cost.
The decision rule for constrained optimization is to select the level for each activity at which
marginal benefit per dollar of marginal cost is equal across all activities.
A continuous choice variable
none of the above
A restaurant hires cooks and waiters. Cooks earn $10 an hour; waiters earn $5 an hour. The manager, who wants to maximize the number of meals served given a fixed payroll of $45 per hour, expects the following from cooks and waiters: Given the above information, the manager should hire
none of the above
An agency is having problems with personal phone calls made during working hours. Each minute of a personal call costs the agency $0.50 in wasted wages. The agency hires operators to monitor calls in order to attain the optimal number of personal calls (minimize total cost of personal calls). Based on the above information, what is the most the agency would be willing to pay the first operator?
none of the above
Based on the above information, what is the most the agency would be willing to pay the fifth operator?
none of the above
If profits depend on both how much is produced (output) and the level of quality, then a profit-maximizing firm should choose the levels of output and quality at which
none of the above
What is the marginal cost for the 5th unit of the activity? 180
none of the above
What is the marginal cost of the 1st unit of the activity?
none of the above
The function a decision maker seeks to maximize or minimize is the ________ function.
objective
Whenever the additional revenue from the last unit of output exceeds the additional cost of that unit, a profit-maximizing firm should
produce more in order to increase profits.
A publishing house is using 400 printers and 200 printing presses to produce books. The printers' wage rate is $20 and the price of a printing press is $100. The last printer added 20 books to total output, while the last press added 50 books to total output. In order to maximize the number of books published with a budget of $28,000, the publishing house
should use more printers and fewer presses because the last dollar spent on a printer yielded more output than the last dollar spent on a press.
A restaurant currently has two cooks and ten waiters. Cooks earn $10 an hour and waiters earn $5 an hour. The last cook added 40 meals served to total output, while the last waiter added 25 meals served to total output. In order to maximize the number of meals served with a fixed budget, the manager should
should use more waiters and fewer cooks because productivity per dollar is higher for waiters than for cooks.
If the marginal benefits of increasing study time are less than the marginal costs, then
study time should be decreased.
If the decision maker is choosing 200 units of activity A,(marginal benefit vs marginal cost)
the activity could be increased by one unit and net benefits will increase by $10.
If the decision maker is choosing 400 units of activity A,
the activity could be reduced by one unit and net benefits will increase by $10.
Gonzo consumes only two things--coke and hot dogs. We can define the addition to "happiness" of consuming an additional coke as the marginal utility of coke and that for hot dogs as the marginal utility of hot dogs. The prices of coke and hot dogs are fixed and Gonzo has a limited budget. To maximize "happiness" subject to his limited budget, Gonzo should purchase coke and hot dogs so that
the addition to happiness per dollar spent on coke is the same as the addition to happiness per dollar spent on hot dogs.
A firm can maximize profit (net benefit) by choosing to produce that level of output at which
the additional revenue from the last unit sold equals the additional cost of that unit.
A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while the last nurse hired treated 1,000 extra patients in a year. If doctors make $80,000 a year and nurses make $40,000 a year, then
the clinic could serve more patients by hiring fewer doctors and more nurses.
A clinic uses doctors and nurses optimally and is servicing the maximum number of patients given a limited annual payroll. The last doctor hired treated 1,600 extra patients in a year, while the last nurse hired treated 1,000 extra patients in a year. If doctors make $64,000 a year and nurses make $40,000 a year, then
the clinic is making the correct decision
For an unconstrained maximization problem
the decision maker seeks to maximize net benefits.
A computer services center has a problem with "malicious" computer usage. The center's director has decided to hire additional personnel to monitor computer usage. In order to minimize the total cost of the malicious usage, the director should hire the number of monitors at which
the decrease in the cost of malicious usage from the last monitor hired equals the cost of hiring the last monitor.
Based on the above information, if the manager has an annual budget of $140,000 and currently is hiring two engineers and three market researchers, then
the last dollar spent on an engineer yielded more new products than the last dollar spent on a market researcher.
In order to minimize the net cost of pollution reduction, the level of pollution reduction (the amount of a pollutant not released into the environment) should be the level at which
the marginal benefit of reducing pollution equals the marginal cost of reducing pollution.
Given the above info, in order to minimize the NET cost of theft, a firm should choose the level of theft prevention at which
the marginal benefit of theft prevention equals the marginal cost of preventing theft.
If the decision maker is choosing 300 units of activity A,
this level maximizes net benefits.
The optimal level of any activity is that level for which
total benefit exceeds total cost by the greatest amount.
When marginal cost is greater than marginal benefit at the current activity level, the decision maker can increase net benefit by decreasing the activity because
total cost will fall by more than total benefit will fall.
