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Ioana’s Candles produces candles. The fixed monthly production cost is $3,000 and the variable cost per candle is $2.50. The candles sell for $6.25 a piece. What is the break-even volume for the company? What are the total cost, revenue, and profit for selling 1250 candles?
Which of the following is a necessary step in the scientific method?
b. Defining the problem
c. Trial and error
d. Drawing a graph
e. Applying break-even analysis
Gold Star Delicacies makes small-batch jams and jellies. Their workspace and equipment cost them $2600 per month in loans, and operating costs total an additional $700 per week. The variable cost per batch of jam in materials and labor is $350. Each batch can fill 200 bottles and each bottle can sell for $3.75. Find the break-even point for how many batches of jam they must sell in a month, assuming they sell all the bottles from each batch produced. What happens to the break-even point if 8% of the bottles from each batch are wasted and cannot be sold? What happens to the original break-even point if, instead, costs per batch go up by another $75?
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
Should Vulco Rubber Inc. invest in a new production plant? Evaluate the payoff table below using the maximax, maximin, and minimax regret criteria.
Decision Economy improves Economy worsens
Invest in Plant A $140,000 -$30,000
Invest in Plant B $260,000 -$95,000
Do not invest $32,000 $24,000
Bradley Architectural, a primarily residential architectural firm, was just notified of an urgent request for a development proposal on a property. They are almost certain that the proposal will go to a competitor, who has been involved with the project since the beginning, but they have 2 days to bring their ideas to the table if they wish to. They are trying to decide what they should propose, if anything. Determine what choice they should make using the Hurwicz at α = 0.05 and at = 0.1, to represent their pessimism about winning the contract. What are the expected values? What choice should they make if they thought they had an equal chance of winning? What would be the expected value?
Decision Win contract Lose contract
Business proposal $2,542,000 -$24,600
Mixed proposal $2,316,000 -$20,950
Residential proposal $2,150,000 -$2,000
No proposal $0 $0
Jane’s New York Deli is considering expanding into a surrounding neighborhood with a new location. Use the payoff table to determine the expected profit or loss for each location, and determine the optimal purchase.
Purchase Economy improves (0.3) No change (0.3) Falls (0.4)
Newton $6,750 $1,750 -$2,345
Springfield $5,450 $3,420 $600
New Rochford $2,250 $1,850 $850
Acton $7,650 $2,850 -$3,650
Boutique Guitars and Gear carries several types of strings. For one type, each package of strings costs the store $3.50 to purchase, and the store can sell them for $6.50 a piece. He estimates that not having the strings in stock if someone wants them costs him about $0.50 in business goodwill. However, after 6 months the strings start to age and he has to drop the prices to $2.50 per pack to get them to sell. He estimates demand for the strings in the next 6 months using the table below. Generate a payoff table, and compute the expected value for each alternative. How many packs of strings should the guitar shop purchase?
John Smith Framing has noticed that a lot of customers would like to be able to print photographs to frame. But since the store does not have an art printer, customers have to get their photos printed elsewhere. The manager, John, is deciding between three possible printers, estimating their profitability based on what sorts of materials they could print and what the expected demand for those services is. Using the information below, create a decision tree for John Smith Framing and compute the expected value for each printer. Which printer should the framing store purchase?
Location Increasing demand (0.22) Steady (0.68) Falling (0.1)
Magnaprint 430f $10,700 $3,540 $1,200
VistaVox md82 $8,650 $5,480 $3,410
ArtStock Pro 5 $15,450 $2,300 -$2,710
Norrington Airport has begun to take in regional jet flights, and needs to expand its air traffic control facilities. It has received three proposals from different agencies for how it can proceed to modernize its facilities. They make a payoff table, shown below. Calculate the expected values of each choice using the given probabilities.
Decision Increased demand (0.72) Current demand (0.28)
Plan A $34,040 -$325,200
Plan B $65,700 -$126,000
Plan C $12,800 -$96,000
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Construct a Gantt chart for the following set of activities. Indicate the total project completion time and the slack for each activity. Submit a plain text version of your Gantt chart by using dashes to represent activity lengths (e.g., —- for 4 days).
Activity Predecessor Time (days)
1 – 5
2 – 3
3 – 2
4 1, 2, 3 8
5 3 5
6 4, 5 6
7 2 3
8 7 7
9 6,8 3
Using the CPM/PERT network below, with times measured in days, find the critical path and the slack times for each step. What is the project completion time? For each node, the step number is written on top and the time written on the bottom.
Using the activity table below, construct a CPM/PERT network noting the activity numbers and durations. Identify the critical path through the network, determine the project completion time, and determine the slack time for each step. Create your network in Microsoft Word and submit it to your instructor.
Activity Predecessor Time (days)
1 – 15
2 – 7
3 – 2
4 – 5
5 3,4 4
6 5 3
7 1,2 8
8 2,6 12
9 3,7 2
Use the activity table below to determine the expected activity lengths and variances for each of the activities, using the beta distribution.
Time estimates: a, m, b (days)
1 3, 10, 20
2 3 ,5, 8
3 2, 6, 14
4 12, 20, 32
Use the activity table below. Find the project completion time. What fraction of the sum of all task times is spent on the critical path tasks? What is the project cost?
Activity Predecessor Time: (weeks) Cost: ($)
1 – 6 5,500
2 1 7 7,900
3 1 6 7,200
4 1 6 6,900
5 2, 3, 4 8 10,200
6 5 3 3,400
Solve the linear programming problem.
Minimize Z = 42x + 10y
2x + 2y ≥ 80
x + 6y ≥ 200
x, y ≥ 0
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
3x + y ≤ 18
2x + 6y ≤ 30
x,y ≥ 0
Turbo Coolers Inc. builds cooling systems for industrial plants. A Type A cooler takes 80 W of power and can cool 18 liters of fluid per minute under the given conditions. A Type B cooler takes 100 W of power and can cool 60 liters of fluid per minute. A Type A cooler costs $3,500 and a Type B cooler costs $12,000. The factory has up to 1,000 W of power it can supply for cooling, and must cool 300 liters of fluid per minute. How many of each type of cooler should Turbo Coolers Inc. install in the factory to 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. Create your graph using Microsoft Word or Excel and submit it to your instructor.
Trinity Bus Lines wants to maximize the number of passengers it can carry from Far Point to Newtown. Bus A can carry 60 passengers and costs $2,700 per month to run. Bus B can carry 48 passengers and costs $1,800 per month to run. The bus line has a maximum of 12 drivers, and can spend no more than $24,300 per month on running the buses. What is the maximum number of passengers they can carry, and which buses should they purchase? 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.
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.
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