COB 291 Final

True or False: A transshipment node will have to have either demand or supply.

False

True or False: As we increase the RHS of a binding constraint within the range defined by allowable increase and allowable decrease (RHS range), the value of shadow price increases.

False

True or False: At a decision node of any decision tree, the decision maker should always choose the branch with the highest expected value.

False

True or False: Changing the RHS of a constraint changes the slope of the constraint line.

False

True or False: If at least one of the constraint lines is parallel to the objective function of a linear program (LP), it will definitely have alternate optimal solutions.

False

True or False: If the change of the objective function coefficient is within allowable limit of OFC range, the optimal objective function value (OFV) does not change.

False

True or False: In an M/M/1 queue the time until the next arrival depends on how much time has elapsed since the last arrival.

False

True or False: It is a good idea to design a call center with 100% utilization factor so that the employees do not get a chance to spend time sitting idle.

False

True or False: The line for 5x-2y=0 passes through the point (5, 2).

False

True or False: A linear program (LP) can be both unbounded and have alternate optimal solutions.

Flase

True or False: For a particular constraint, if the slack is zero, one would expect the shadow price to be non-zero.

True

True or False: The EVSI will approach EVPI as the accuracy of information increases.

True

True or False: The decision variables are entered as changing variable cells in built-in Excel solver.

True

True or False: The lines 3x-2y=6 and 9x-6y=36 do not intersect each other.

True

A diet is being developed which must contain at least 100 mg of vitamin C. Two fruits are used in this diet- bananas and apples. Suppose each banana contains 30 mg of vitamin C and each apple contains 20 mg of vitamin C. The diet must contain at least 100 mg of vitamin C. Say B is number of bananas and A is number of apples used in the diet. Which of the following constraints reflects the relationship between number of bananas and apples and amount of vitamin C? a. 20A + 30B >- 100 b. 20A + 30B <- 100 c. 20A + 30B = 100 d. 30A + 20B >- 100 e. None of the above

a. 20A + 30B >- 100

In a network problem, the constraint X13 + X23 - X34 >- 50 indicates that a. At least 50 units are required at node 3 b. At least 50 units will be shipped from node 3 c. At least 50 units will be shipped in from node 1 d. At least 50 units must pass through node 3 e. None of the above

a. At least 50 units are required at node 3

A mathematical model is considered to be "valid" when a. the left-hand and right-hand sides of expressions are equal b. it accurately represents the relevant characteristics of the object or decision c. the model is complex and contains intricate details d. it replicates many aspects of the object or decision

b. it accurately represents the relevant characteristics of the object or decision

In an M/M/1 queue, if the server can serve 12 customers per hour on an average, what is the variance (σ^2) of service time (if time is in minutes)? Hint: Exponential distribution has the same mean and standard deviation (σ). a. 5 b. 12 c. 25 d. 144

c. 25

The unit costs of forty watt, sixty watt, and hundred watt electric bulbs are $0.25, $0.50, and $2.00 respectively. The dollar values of three different bulb inventories in an electrical supply store are given below: F = dollar value of forty watt bulbs S = dollar value of sixty watt bulbs H = dollar value of hundred watt bulbs The total number of bulbs in the store is: a. F + S + H b. 0.25F + 0.5S + 2H c. 4F + 2S + 0.5H d. 25F + 50S + 200H e. None of the above

c. 4F + 2S + 0.5H

Let Pij = production level of product i in period j. In order to specify that production levels of product 1 in periods 3 and 4 differ by no more than 100 units, which constraints should be used? a. P13 - P14 <- 100; P13 - P14 >- 100 b. P13 - P14 <- 100; P14 - P13 >- 100 c. P13 - P14 <- 100; P14 - P13 <- 100 d. P13 - P14 >- 100; P14 - P13 >- 100 e. None of the above

c. P13 - P14 <- 100; P14 - P13 <- 100

If arrivals occur every 20 minutes according to a Poisson process, then which is NOT true? (Mean arrival rate is λ) a. λ = 3 arrivals per hour b. λ = 1/20 arrivals per minute c. λ = 20 arrivals per hour d. λ = 72 arrivals per day

c. λ = 20 arrivals per hour

Two types of machine parts: Part A and Part B are made in a particular production line. These products are not made simultaneously. The cost of making one unit of Part A and one unit of Part B are $4 and $6, respectively. It takes 5 minutes to make unit of Part A and 10 minutes to make one unit of Part B. Let NPA = number of Part A made and NPB = number of Part B made. The expression for total time taken (in hours) to make NPA units of Part A and NPB units of Part B is: a. 4 NPA + 6 NPA b. 5 NPA + 10 NPB c. (1/5) NPA + (1/10) NPB d. (1/12) NPA + (1/6) NPB e. None of the above

d. (1/12) NPA + (1/6) NPB

Let A, B, and C be the money invested in companies A, B, and C, respectively. If no more than 50% of the total investment ($) can be in company B, then a. B <- 0.5 b. A - 0.5B + C <- 0 c. 0.5A - B - 0.5C <- 0 d. -0.5A + 0.5B - 0.5C <- 0 e. None of the above

d. -0.5A + 0.5B - 0.5C <- 0

A whole seller packs vests in a pack of 4 and sells the pack at a price of $6. The yearly fixed cost is $2500. The whole seller buys vests from a vest maker at a price of $1 per vest. Assume the whole seller can sell all vests that are bought. How many packs of vests does the shopkeeper need to sell to make $1500 profit in a year? a. 750 b. 1000 c. 1250 d. 2000

d. 2000

The expected expenditure of the transportation and distribution division of a small retailer was $300,000. After adopting few efficient measures recommended by a management consulting firm, the new expected expenditure including the consulting fee of $15,000 was estimated to be $250,000. The EVSI is a. -35,000 b. 35,000 c. 50,000 d. 65,000

d. 65,000

Which command is equivalent to =SUMPRODUCT(A1:A3,B1:B3)? a. =SUM(PRODUCT((A1:A3,B1:B3)) b. =PRODUCT(SUM(A1:A3,B1:B3)) c. PRODUCT(A1+B1,A2+B2,A3+B3)) d. A1*B1 + A2*B2 + A3*B3 e. None of the above

d. A1*B1 + A2*B2 + A3*B3

Department 3 initially has 2500 hours. Transfers are allowed to departments 2 and 4, and from departments 1 and 2. If Tij measures the hours transferred from department i to department j and Ai measures the labor hours allocated to department i after the transfers, then a. T13 + T23 - T32 - T34 - A3 =2500 b. T31 + T32 - T23 - T43 + A3 = 2500 c. A3 + T13 + T23 - T32 - T34 = 2500 d. A3 - T13 - T23 + T32 + T34 = 2500 e. None of the above

d. A3 - T13 - T23 + T32 + T34 = 2500

Let M be the number of units to make and B be the number of units to buy. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function is a. Max: 2M + 3B b. Min: 4000(M+B) c. Max: 8000M +12000B d. Min: 2M + 3B e. None of the above

d. Min: 2M + 3B

You are considering starting a wholesale business of paper rolls. In this business, you would buy paper rolls from a manufacturer at a price of $100 per lot, store it for a while which would cost around $20 per lot, and then sell the rolls to the retailers. Your revenue from the sales to retailers depends on the market condition. Revenue from a lot will be $140, $130, and $115 under good, fair, and poor market conditions, respectively. The chances of good, fair, and poor market conditions prevailing are 20%, 35%, and 45%, respectively. Suppose you draw a decision tree for this. How would you describe this tree? a. One decision node and no chance nodes b. One decision node and three chance nodes, with the decision node coming first c. One decision node and one chance node, with the chance node coming first d. One decision node and one chance node, with the decision node coming first e. Three decision nodes and one chance node, with the chance node coming first

d. One decision node and one chance node, with the decision node coming first

An appliance manufacturing company makes two types of fans: table fan (T) and pedestal fan (P). If they need to make at least 20 table fans and 30 pedestal fans, the constraint(s) should be: a. T + P <- 50 b. T + P >- 50 c. T >- 30, P >- 20 d. T >- 20, P >- 30 e. T >- 20, P >- 30, (T + P) <- 50

d. T >- 20, p >- 30

Two types of machine parts: Part A and Part B are made in a particular production line. These products are not made simultaneously. The cost of making one unit of Part A and one unit of Part B are $4 and $6, respectively. It takes 5 minutes to make unit of Part A and 10 minutes to make one unit of Part B. Let NPA = number of Part A made and NPB = number of Part B made. Both Part A and Part B use a common resource and the corresponding constraint for the resource consumption is 5 NPA + 10 NPB <- 200. If 20 units of Part A and 4 units of Part B are made, how many units of the resource remain unused? a. 200 b. 185 c. 140 d. 100 e. None of the above

e. None of the above

If the allowable increase for a constraint with shadow price of 1 is 100 and we add 110 units of the resource, what happens to the objective function value? a. increase of 10 b. increase of 100 c. increase of 110 d. no change e. cannot answer without resolving the LP

e. cannot answer without resolving the LP