# Operational research

1. The Black Diamond Board Company produces snowboards. The fixed monthly production cost is \$15,000 and the variable cost per snowboard is \$35. The snowboards sell for \$130 a piece. What is the break-even volume for the company? What is the total cost, revenue, and profit for selling 210 boards? (Points : 4)

Question 2. 2. Management science is (Points : 2)
a new and poorly established discipline in business.
a philosophy of approaching problems in a logical manner.
just a collection of techniques.
fundamentally different from operations research.
credited with decreasing the efficiency of business firms.
Question 3. 3. Julia makes handmade wreaths. Her fixed costs for equipment and workspace are \$350 per week. The variable cost per wreath in materials is \$13. She sells the wreaths for \$28 each. Find the break-even point for how many wreaths she must sell in a month. How much profit does she make in a month if she sells 73 wreaths? (Points : 3)

Question 4. 4. Bradley is trying to decide if he should buy a new mower for his business. Select the best decision using the maximax and maximin criteria using the payoff table below.

Decision Economy improves Economy worsens
Don’t buy mower \$5,250 \$2,400 (Points : 3)

Question 5. 5. Should Jonathan buy a new computer? Evaluate the payoff table below using the maximin and minimax regret criteria.

Decision New job No new job
Don’t buy computer \$1,225 \$1,225 (Points : 4)

Question 6. 6. Stephanie runs a hair salon. She is trying to decide if she should hire another hairdresser. Determine what choice she should make using the Hurwicz (a = 0.4) and equal likelihood criteria.

Hire \$4,175 -\$1,600
Do not hire \$2,440 \$1,954 (Points : 4)

Question 7. 7. Jericho Toolshop is considering purchasing another power tool. Use the payoff table to determine the expected profit or loss for each purchase, and determine the optimal purchase.

Purchase Gain clients (0.3) No change (0.5) Lose clients (0.2)
Bandsaw \$2,450 \$1,875 -\$400
Table saw \$5,560 \$700 -\$3,450
Router \$1,900 \$1,200 -\$260
Sander \$1,550 \$960 \$430 (Points : 5)

Question 8. 8. Maurice’s Gift Shop stocks holiday themed paperweights from a local glass supplier. Each paperweight costs Maurice a total of \$12, and he can sell them for \$18 a piece. After the holidays he will only be able to sell them for \$10 a piece. He estimates demand for the paperweights in the table below. Generate a payoff table, and compute the expected value for each alternative. How many paperweights should Maurice purchase?

Demand Probability
8 0.10
9 0.15
10 0.30
11 0.25
12 0.15
13 0.05 (Points : 8)

Question 9. 9. The Corner Bakery is going to move its location. The staff are deciding between three different locations by estimating their profitability at each. Using the information below, create a decision tree for the Corner Bakery and compute the expected value of each location. Which one should the bakery relocate to?

Location Good economy (0.3) Poor economy (0.7)
10th Street \$4,350 \$3,670
Park Avenue \$5,250 \$3,540
Shepard Way \$8,975 \$1,200 (Points : 5)

Question 10. 10.
Dragonfly Publishing is considering purchasing more warehouse space and more machinery to allow it to print more books and magazines. The group creates a payoff table to express their likely profit for each purchase given the state of the market. The payoff table is shown below. Calculate the expected value of each outcome using the given probabilities.
Purchase Solid market (0.6) Declining market (0.4)
Largest space \$75,000 -\$22,500
Smallest space \$58,500 \$10,500
No purchase \$43,350 \$26,200
(Points : 6)

Question 11. 11. Construct a Gantt chart for the following set of activities. Indicate the total project completion time and the slack for each activity. Submit a plain text version of your Gantt chart by using dashes to represent activity lengths (e.g., —- for 4 weeks).
Activity Predecessor Time (weeks)
1 – 3
2 – 4
3 1 5
4 1 4
5 3 8
6 2 2
7 4 5
(Points : 4)

Question 12. 12. Using the CPM/PERT network below, with times measured in days, find the critical path and the slack times for each step. For each node, the step number is written on top and the time written on the bottom.

(Points : 5)

Question 13. 13. Using the activity table below, construct a CPM/PERT network noting the activity numbers and durations. Identify the critical path through the network, and determine the project completion time. Create your network in Microsoft Word and submit it to your instructor.
Activity Predecessor Time (weeks)
1 – 8
2 – 3
3 – 3
4 1, 2 4
5 3, 4 6
6 5 2
7 1 5

(Points : 6)

Question 14. 14.
Use the activity table below to determine the expected activity lengths and variances for each of the activities, using the beta distribution.

Activity Time estimates: a, m, b (months)
1 2, 4, 8
2 1 ,2, 4
3 6, 8, 14
4 4, 5, 7
(Points : 5)

Question 15. 15. Use the activity table below. Find the normal project completion time. Find the cost.
Activity Predecessor Time (weeks) Cost (\$)
1 – 6 8,900
2 1 5 7,800
3 1 8 10,500
4 3 4 4,200
5 2, 4 5 5,100
(Points : 4)

Question 16. 16. Solve the linear programming problem.

Maximize Z = 35x + 60y
subject to
x + 2y = 35
5x + 4y = 100
x, y = 0
(Points : 4)

Question 17. 17. Solve the linear programming problem by graphing. Graph the feasible region, list the extreme points and identify the maximum value of Z. You do not have to submit your graph, but please list the equations of the lines that form the feasible region.

Maximize Z = 22x + 12y
subject to
3x + y = 18
x + 4.5y = 36
x,y = 0
(Points : 5)

Question 18. 18.
Way of Nature Co. produces granolas marketed as being high in vitamins and minerals. An ounce of oats provides 8 milligrams of vitamin A. An ounce of quinoa provides 4 milligrams of vitamin A. An ounce of oats costs \$0.05 and an ounce of quinoa costs \$0.07. A box of the granola needs to contain at least 56 milligrams of vitamin A and must use no more than 3.5 ounces of oats. How many ounces of each ingredient should Way of Nature Co. use to meet this requirement and minimize cost? Formulate a linear programming model for this situation. Solve this model using graphical analysis. Display your graph and the solution parameters. Create your graph using Microsoft Word or Excel and submit it to your instructor.
(Points : 6)

Question 19. 19. Human Interactions Corporation produces two products using two assembly lines. Line A has 140 hours available this month while Line B has 80 hours available. On Line A, Product 1 requires 10 hours of production time and Product 2 requires 8 hours of production time. Only Product 2 needs to be finished on Line B, and takes 8 hours of time. When completed, the profit per unit for Product 1 is \$60 and for Product 2 is \$40. Formulate a linear programming model to solve this problem. List the extreme points and determine the solution graphically. You do not need to submit your graph.
(Points : 6)

Question 20. 20.
The neighborhood food collective produces jams and sells them to benefit local food banks. The collective produces a strawberry-rhubarb jam, and a strawberry-orange jam. The maximum number of jars of jam they can produce in their current space is 302. They do not have enough oranges to produce more than 134 jars of strawberry-orange jam. The collective can sell a jar of strawberry-rhubarb jam for a profit of \$2.50, and a jar of strawberry-orange jam for a profit of \$2.75. How many jars of each should the collective make to maximize its donation to the food bank? Formulate a linear programming model and solve it graphically. You do not need to submit your graph.
(Points : 7)

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