BA 260 Chapter 12

Ms. Ward plans to open a pizza bistro and name it Ward's Pizza. As owner, Ms. Ward wants this venture to be as successful and as profitable as possible. She needs to determine how many employees to schedule for a given shift and must keep the wage cost as low as possible. Ms. Ward decides on the following pay rates: Crew members (C) will be hired at $8.00 per hour, shift supervisors (S) at $10.00 per hour, and assistant managers (M) at $15.00 per hour. Ms. Ward's business plan includes one assistant manager working each shift and one shift supervisor for every five crew members. Ms. Ward has been advised that at least seven crew members are needed to work each shift. We would like to minimize the employee wages while still meeting customer demand. Suppose the ideal combination is to run a shift with 1 assistant manager, 2 shift supervisors, and 10 crew members. What is Ms. Ward's hourly wage expense?

$115/hour

Zapit, Inc. manufactures two products, Product A and Product B. Product A yields an incremental profit of $2 per unit, and Product B yields an incremental profit of $4. Product A requires four hours of processing at Machine A and two hours at Machine B. Product B requires six hours at Machine A, six hours at Machine B, and one hour at Machine C. Machine A has a maximum of 120 hours of available capacity per day, Machine B has 72 hours, and Machine C has 10 hours. If the company produces 562 of Product A and 636 of Product B, calculate the expected profit?

$3,668

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit.If the numbers of G1 and T1 models manufactured by the company in a week are 100 and 150 units respectively, determine the total profit generated by the company in a week.

$35,500

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 units manufactured per week are ____ and ______ units respectively, the number of labor hours used by the production department is 1962.5 labor hours per week.

155, 355

Zapit, Inc. manufactures two products, Product A and Product B. Product A yields an incremental profit of $2 per unit, and Product B yields an incremental profit of $4. Product A requires four hours of processing at Machine A and two hours at Machine B. Product B requires six hours at Machine A, six hours at Machine B, and one hour at Machine C. Machine A has a maximum of 120 hours of available capacity per day, Machine B has 72 hours, and Machine C has 10 hours.If the company wishes to maximize profit, what is the objective function?

2A + 4B

Zapit, Inc. manufactures two products, Product A and Product B. Product A yields an incremental profit of $2 per unit, and Product B yields an incremental profit of $4. Product A requires four hours of processing at Machine A and two hours at Machine B. Product B requires six hours at Machine A, six hours at Machine B, and one hour at Machine C. Machine A has a maximum of 120 hours of available capacity per day, Machine B has 72 hours, and Machine C has 10 hours.Which one is NOT a constraint?

2A + 4B ≤ 120

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes the assembly's department's labor constraint for a week is

2G + 1.5T ≤ 875.

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes the production department's labor constraint for a week is

3.5G + 4T ≤ 2030.

A local bar manager has a marketing budget of $320. He decides to purchase an ad from a local TV station and a local newspaper. TV ads cost of $80 per ad. Newspaper ads cost of $40 per ad. It is estimated that each TV ad would draw in 5 new customers, which equates to an additional profit of $50 per day. It is also estimated that each newspaper ad would draw in 2 new customers, which equates to an additional profit of $20 per day. What is the objective function?

50T + 20N

Ms. Ward plans to open a pizza bistro and name it Ward's Pizza. As owner, Ms. Ward wants this venture to be as successful and as profitable as possible. She needs to determine how many employees to schedule for a given shift and must keep the wage cost as low as possible. Ms. Ward decides on the following pay rates: Crew members (C) will be hired at $8.00 per hour, shift supervisors (S) at $10.00 per hour, and assistant managers (M) at $15.00 per hour. Ms. Ward's business plan includes one assistant manager working each shift and one shift supervisor for every five crew members. Ms. Ward has been advised that at least seven crew members are needed to work each shift. We would like to minimize the employee wages while still meeting customer demand. What is the objective function?

8C + 10S + 15M

Consider the following Linear Programming Model and its associated spreadsheet model. Let A = the number of individual pizzas that can be made and B = the number of large pizzas that can be made. We make a profit of $3 for each individual pizza and a profit of $9 for each large pizza that we sell. We would like to maximize our profit function, 3A + 9B, subject to the constraints 1A + 4B ≤ 24 and 1A + 2B ≤ 16. Refer to the image of the spreadsheet below. What formula should be entered in cell D4 to compute total profitability?

= B3*B4 + C3*C4

Consider the following Linear Programming Model and its associated spreadsheet model. Let A = the number of individual pizzas that can be made and B = the number of large pizzas that can be made. We make a profit of $3 for each individual pizza and a profit of $9 for each large pizza that we sell. We would like to maximize our profit function, 3A + 9B, subject to the constraints 1A + 4B ≤ 24 and 1A + 2B ≤ 16. Refer to the image of the spreadsheet below. Which cell(s) specifies the "Changing Variable Cells" in Excel Solver?

B2:C2

Consider the following Linear Programming Model and its associated spreadsheet model. Let A = the number of individual pizzas that can be made and B = the number of large pizzas that can be made. We make a profit of $3 for each individual pizza and a profit of $9 for each large pizza that we sell. We would like to maximize our profit function, 3A + 9B, subject to the constraints 1A + 4B ≤ 24 and 1A + 2B ≤ 16. Which cell(s) designates the objective function as specified in Excel Solver?

D4

The goal of business analytics is to provide information to management for improved decision making. If a linear program has more than one optimal solution, you should determine which decision seems optimal and provide that solution to management.

False

The objective function value will vary according to each alternate optimal point.

False

Ms. Ward plans to open a pizza bistro and name it Ward's Pizza. As owner, Ms. Ward wants this venture to be as successful and as profitable as possible. She needs to determine how many employees to schedule for a given shift and must keep the wage cost as low as possible. Ms. Ward decides on the following pay rates: Crew members (C) will be hired at $8.00 per hour, shift supervisors (S) at $10.00 per hour, and assistant managers (M) at $15.00 per hour. Ms. Ward's business plan includes one assistant manager working each shift and one shift supervisor for every five crew members. Ms. Ward has been advised that at least seven crew members are needed to work each shift. We would like to minimize the employee wages while still meeting customer demand. Define the employee constraints per shift.

M = 1, S =5C, C ≥ 7

Ms. Ward plans to open a pizza bistro and name it Ward's Pizza. As owner, Ms. Ward wants this venture to be as successful and as profitable as possible. She needs to determine how many employees to schedule for a given shift and must keep the wage cost as low as possible. Ms. Ward decides on the following pay rates: Crew members (C) will be hired at $8.00 per hour, shift supervisors (S) at $10.00 per hour, and assistant managers (M) at $15.00 per hour. Ms. Ward's business plan includes one assistant manager working each shift and one shift supervisor for every five crew members. Ms. Ward has been advised that at least seven crew members are needed to work each shift. We would like to minimize the employee wages while still meeting customer demand. Which variable is NOT a decision variable?

P = profit in dollars

Suppose a transportation problem consisted of three manufacturing plants, or origins (1 - Minneapolis, 2 - St. Louis, and 3 - Pittsburgh) and 4 distribution centers, or destinations (1 - San Francisco, 2 - Houston, 3 - Tampa, and 4 - Charlotte). Using standard double-scripted notation, what is the city of origin and destination for the variable? x32?

Pittsburgh to Houston

Zen Inc. manufactures two types of products, the G1 and the T1 model airplane. The manufacturing process consists of two principal departments: production and assembly. The production department has 58 skilled workers, each of whom works 7 hours per day. The assembly department has 25 workers, who also work 7-hour shifts. On an average, to produce a G1 model, Zen Inc. requires 3.5 labor hours for production and 2 labor hours for assembly. The T1 model requires 4 labor hours for production and 1.5 labor hours in assembly. The company anticipates selling at least 1.5 times as many T1 models as G1 models. The company operates five days per week and makes a net profit of $130 on the G1 model, and $150 on the T1 model. Zen Inc. wants to determine how many of each model should be produced on a weekly basis to maximize net profit. If the numbers of G1 and T1 products produced each week are denoted as G and T respectively, the function that describes Zen, Inc.'s sales prediction for a week is

T - 1.5G ≥ 0.

A linear programming model has the following objective function: Maximize: A + 3AB + 4B. This model violates what key linear programming model assumption?

The model is not a linear function.

A local bar manager has a marketing budget of $320. He decides to purchase an ad from a local TV station and a local newspaper. TV ads cost of $80 per ad. Newspaper ads cost of $40 per ad. It is estimated that each TV ad would draw in 5 new customers, which equates to an additional profit of $50 per day. It is also estimated that each newspaper ad would draw in 2 new customers, which equates to an additional profit of $20 per day. True or false: The number of TV ads and newspaper ads are the decision variables for this formulation.

True

It is possible for a linear program to have more than one optimal solution.

True

Shadow prices are found in sensitivity analysis of linear programming solutions.

True

Maximize Z = 3X + Y subject to the following constraints:12X + 14Y ≤ 85,3X + 2Y ≤ 18,Y ≤ 4.Which of the following extreme points yields the maximum value?

X = 6, Y = 0

"Changing Variable Cells" in Solver refers to the

decision variables.

When using Solver, the parameter "Changing Variable Cells" is typically associated with the

decision variables.

In the graphical solution procedure, the region bound by the set of constraints is called the solution's

feasible region.

The general approach for trying to find an alternative optimal solution to a linear program is: Solve the linear program. Make a new objective function of the sum of the variables that were equal to zero in the original solution. Then add a constraint that forces the original objective function to be equal to the optimal objective function value from the original solution. Solve the reformulated problem. Finally, If the objective function value of the reformulated problem is ______, you have found an alternative optimal solution.

greater than zero

Graphically, _______________ means that no points satisfy all the constraints and the nonnegativity conditions simultaneously.

infeasibility

A linear programming problem has the following two constraints: X ≤ 20 and X ≥ 25. This problem is

infeasible

If an optimal solution cannot be found that satisfies all the constraints of the linear programming, it is said to be

infeasible.

With two-variable problems, extreme points are determined by the _______________ of the constraint lines.

intersection

A linear programming model has the following objective function: Maximize: A2 + 3B + 4C. This model violates what key linear programming model assumption?

it is not a linear function

A linear programming problem has the following constraint: 6.0A + 2.7B + 7.3C ≤ 650, where A, B, and C are decision variables of the problem. The constraint function is the

left-hand side of the expression.

Making a binding constraint _________ restrictive degrades or leaves unchanged the __________.

less, optimal objective function value

Making a binding constraint __________ restrictive improves or leaves unchanged the ________.

less, optimal objective function value

Alternative optimal solutions is the case in which

more than one solution provides the optimal value for the objective function.

A feasible solution to a linear programming problem

must satisfy all of the problem's constraints simultaneously.

A graphical display that can be used to show the options for distribution routes, including origin and destination points as well as chipping routes is called a

network.

Optimization models can be linear. They can also be

nonlinear.

To enter decision variables as a block in Solver

the cells denoting the decision variables must be next to each other.

"Objective Cell" in Excel Solver refers to the

the objective function.

The algorithm that Excel Solver uses to solve linear programs by systematically finding which set of constraints form the optimal extreme point of the feasible region is

the simplex method.

The graphical method of Linear Programming can handle only _____________ decision variables.

two

A message in the Excel Solver Results dialog box telling you that the "Objective Cell values do not converge" is given when you attempt to solve a(n) _______________ problem.

unbounded

If a profit maximization problem results in a(n) ________________ solution, the mathematical model does not represent the real-world problem sufficiently.

unbounded

If the solution to a linear program is ________, no optional solution to the problem can be found.

unbounded

If the value of the solution may be made infinitely small in a minimization problem without violating any of the constraints, it is said to be

unbounded.

When naming decision variables, there are advantages to using a general notation that can be expanded to accommodate any number of decision variables. The general notation that is recommended for linear programs is

x1, x2, x3 ...