Questions -
Question 1 - Elderwood Tree Farm grows and sells landscaping trees. The fixed monthly cost of land and equipment is $6,450 and the variable cost per tree is $36. The trees sell for $75 apiece. What is the break-even volume for the company? What are the total cost, revenue, and profit for selling 182 trees?
Question 2 - Which is true in general of management science mathematical techniques and equations?
a. Parameters are unknowns from the problem environment.
b. Data are constant values that are generally coefficients of the variables in the equations.
c. The variable whose value we want to find is the decision variable.
d. Each resource equation represents an objective function in the problem.
e. The profit equation takes the form of a subjective function.
Question 3 - Laura and Tyler make handmade and hand-painted tables. Their fixed costs for equipment and workspace are $70 per week. The variable cost per table in wood, paint, and other materials is $36. They believe they can sell the tables for $45 each. Find the break-even point for how many tables they must sell in a month. How much profit do they make in a month if they sell 12 tables? What is their new monthly break-even point if they improve their workmanship so they can sell the tables for $99 each? What would they make if they sold 12 tables in a month now?
Question 4 - Jessica is trying to decide if she should buy a new van for her business. Select the best decision using the maximax and maximin criteria using the payoff table below.
|
Decision
|
Economy improves
|
Economy worsens
|
|
Buy large van
|
$26,000
|
-$3,400
|
|
Buy small van
|
$20,500
|
-$60
|
|
Don't buy van
|
$15,200
|
$8,400
|
Question 5 - Should Kaylee go to college or start working right away? She estimates her 10-year gross income for several choices given different possibilities for the state of the economy. Evaluate the payoff table below using the maximin and minimax regret criteria.
|
Decision
|
Economy improves
|
Steady
|
Declines
|
|
Attend 4-year college
|
$270,000
|
$240,000
|
$190,000
|
|
Attend 2-year college
|
$310,000
|
$280,000
|
$230,000
|
|
Don't attend college
|
$290,000
|
$250,000
|
$220,000
|
Question 6 - Delicatessen Catering Co. provides catering services for weddings, reunions, business functions, and a variety of other social events. Delicatessen is thinking of hiring more staff to keep up with rising demand. This would require purchasing more equipment and vehicles to ensure these staff can do their jobs. Determine what choice they should make using the Hurwicz (a = 0.7 and a = 0.4) and equal likelihood criteria. What are the expected values?
|
Decision
|
Increased demand
|
Decreased demand
|
|
Hire staff
|
$20,040
|
-$18,950
|
|
Do not hire
|
$5,650
|
$4,970
|
Question 7 - Blackbird Brownies and Confections is looking to hedge its bets in the face of economic uncertainty and ensure that it can continue to grow. The company hires a business analyst to identify four different business investments they could make with 25% of their current cash to help them continue to grow through a recession. Use the payoff table to determine the expected profit or loss for each choice, and determine the optimal investment.
|
Investment
|
Economy gains (0.1)
|
Steady (0.3)
|
Declines (0.6)
|
|
Revamp distribution
|
$12,860
|
$4,200
|
$3,450
|
|
Revamp kitchens
|
$12,040
|
$6,960
|
$1,200
|
|
Online store
|
$10,950
|
$8,660
|
$450
|
|
Mobile sales truck
|
$15,600
|
$13,480
|
-$9,850
|
Question 8 - Green Thumb Garden Supply orders plants to sell to its customers. Each plant costs $23 to purchase and another $15 to grow and feed for the season. The plants will be sold for $65 a piece. Once the season is over, the remaining plants will be sold for just $25. The company estimates demand for the plants in the table below. Generate a payoff table, and compute the expected value for each alternative. What is the expected value for perfect information? How many plants should the garden supply company purchase?
|
Demand
|
Probability
|
|
22
|
0.15
|
|
23
|
0.25
|
|
24
|
0.25
|
|
25
|
0.25
|
|
26
|
0.10
|
Question 9 - Hyperware Tool & Die manufactures parts for an electric motor. Lately their customer has discovered that one of the pieces develops stress fractures during use. Hyperware has several options for how to fix this. They can change the alloy used for the part, which gives them two alloy possibilities. Their engineers estimate that the chances of success are 65% if they change the alloy. The other possibility is that they could change the design of the part, which provides two design possibilities. Their engineers estimate that either one presents a 95% chance of fixing the problem. However, this will require changes to the production process and will be more expensive. Using the information below, create a decision tree for Hyperware Tool & Die and compute the expected value for each change. How should Hyperware respond to the stress fractures?
Approaches:
|
Change alloy
|
Success (0.65)
|
Failure (0.35)
|
|
Alloy A
|
-$6,340
|
-$25,545
|
|
Alloy B
|
-$7,450
|
-$23,500
|
|
|
|
Redesign part
|
Success (0.95)
|
Failure (0.05)
|
|
Design A
|
-$10,550
|
-$35,950
|
|
Design B
|
-$12,680
|
-$32,100
|
Question 10 - Delaware Coffee Roasters, LLC. is considering moving its coffee roasting operation from the back of the store to some neighboring warehouse space. The company has to decide how much space to rent and how to handle sales and distribution. They make a payoff table, shown below. Determine the expected value for each alternative using the given probabilities.
|
Acquire
|
Stable economy (0.65)
|
Slowing economy (0.35)
|
|
4000 sq. ft, new trucks
|
$105,000
|
-$65,450
|
|
4000 sq. ft, keep trucks
|
$84,200
|
-$25,300
|
|
2000 sq. ft, new trucks
|
$74,350
|
-$38,900
|
|
2000 sq. ft, keep trucks
|
$56,750
|
-$15,250
|
Question 11 - Construct a Gantt chart for the following set of activities. Indicate the total project completion time and the slack for each activity. Submit a plain text version of your Gantt chart by using dashes to represent activity lengths (e.g., ---- for 4 months).
|
Activity
|
Predecessor
|
Time (months)
|
|
1
|
-
|
6
|
|
2
|
-
|
8
|
|
3
|
1
|
4
|
|
4
|
1
|
3
|
|
5
|
2,3
|
7
|
|
6
|
4,5
|
1
|
|
7
|
6
|
5
|
|
8
|
7
|
4
|
Question 12 - Using the CPM/PERT network below, with times measured in months, find the critical path and the slack times for each step. What is the project completion time? For each node, the step number is written on top and the time written on the bottom.
Question 13 - Using the activity table below, construct a CPM/PERT network noting the activity numbers and durations. Identify the critical path through the network, determine the project completion time, and determine the slack time for each step. Create your network in Microsoft Word and submit it to your instructor.
|
Activity
|
Predecessor
|
Time (days)
|
|
1
|
-
|
15
|
|
2
|
-
|
7
|
|
3
|
-
|
2
|
|
4
|
-
|
5
|
|
5
|
3,4
|
4
|
|
6
|
5
|
3
|
|
7
|
1,2
|
8
|
|
8
|
2,6
|
12
|
|
9
|
3,7
|
2
|
Question 14 - The activity table below corresponds to a project with critical path 1 → 4 → 5 → 6 → 8. Find the mean lengths and variances of each task on the critical path.
|
Activity
|
Times (days)
|
|
a
|
m
|
b
|
|
1
|
6
|
10
|
12
|
|
2
|
4
|
9
|
14
|
|
3
|
3
|
7
|
20
|
|
4
|
4
|
5
|
8
|
|
5
|
1
|
3
|
7
|
|
6
|
11
|
13
|
16
|
|
7
|
8
|
10
|
12
|
|
8
|
3
|
6
|
8
|
Question 15 - Use the activity table below. Find the project completion time. What is the total cost for all tasks on the critical path only?
|
Activity
|
Predecessor
|
Time (days)
|
Cost ($)
|
|
1
|
-
|
3
|
300
|
|
2
|
1
|
2
|
350
|
|
3
|
2
|
10
|
1,250
|
|
4
|
2
|
6
|
880
|
|
5
|
3
|
5
|
675
|
|
6
|
4,5
|
3
|
325
|
Question 16 - Solve the linear programming problem.
Minimize Z= 42x+ 10y
subject to
2x + 2y ≥ 80
X + 6y ≥ 200
x, y ≥ 0
Question 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 = 14x+ 6y
subject to
3x + y ≤ 18
2x + 6y ≤ 30
x, y ≥ 0
Question 18 - FireBurst Electronics produces memory units for specialized applications. Unit A provides 2 GB of high-bandwidth memory and 18 GB of low-bandwidth memory. Unit B provides 0.5 GB of high-bandwidth memory and 60 GB of low-bandwidth memory. Unit A costs $12.50 and Unit B costs $7.50. A particular application requires at least 35 GB of high-bandwidth memory, and 648 GB of low-bandwidth memory. How many of each memory unit should FireBurst Electronics use to meet this requirement and minimize the cost of the product? 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.
Question 19 - Old Japan Pottery Co. produces glazed bowls and jugs using two furnaces, one to fire the clay and another to set the glaze. A bowl takes 2 hours to fire in the first furnace, and 1.5 hours for the glaze to set in the second furnace. A jug takes 3 hours to fire in the first furnace, and does not need to glaze in the second furnace. The first furnace has 42 hours of available time, while the second furnace has 22.5 hours of available time. A bowl sells for $30 and a jug sells for $42. How many bowls and jugs should they create to maximize their gross profit? 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.
Question 20 - Three Ships Winery produces two different wine blends. A batch of the Dark Night blend uses 4 tons of malbec grapes and 2 tons of merlot grapes. A batch of the Morning Star blend uses 2 tons of malbec grapes and 4 tons of merlot grapes. The winery has a total of 18 tons of malbec grapes, and 18 tons of merlot grapes.The profit for a batch of Dark Night is $14,500 and the profit for a batch of Morning Star is slightly less at $12,250. How many batches of each type of wine should the winery produce this year to maximize its profit, assuming half batches are allowed? Formulate a linear programming model and solve it graphically. Display your graph and calculate the maximum profit. Create your graph using Microsoft Word or Excel and submit it to your instructor.