Operation Management-QA69 online

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LP Advanced Application

Jeep Wranglers are one of the sturdiest cars but have a tendency to tip over on sharp or uneven terrains. As a result, the customers can decide to install extra roll bars on their Jeeps for safety considerations, especially if they are likely to drive the jeep on mountainous terrain.

Kito Industries manufactures two types of roll bars for Jeeps. Model A is installed to the jeep using the existing holes in the jeep’s frame. Model Z is a heavier roll bar that must be welded to the jeep frame externally. Model A requires 15 pounds of a special type of steel alloy, 30 minutes of manufacturing time and 80 minutes of assembly time. Model Z requires 20 pounds of the steel alloy, 45 minutes of manufacturing time, and 100 minutes of assembly time. Kito’s steel supplier indicated that at most 35,000 pounds of steel alloy will be available next quarter. Moreover, Kito estimates that 1500 hours of manufacturing time and 2000 hours of assembly time will be available next quarter. The profit contributions are $ 180 per unit for Model A and $250 per unit for Model Z. Given the nature of the demand, Kito Industries determines that at least 200 Model A frames have to be produced. The linear programming model for this problem is as follows

Let A = Model A Roll Bar Frame

Z = Model Z Roll Bar Frame

Max 180A + 250Z

s.t.

15A + 20Z ≤ 35,000 Steel available

30A + 45Z ≤ 1500*60 Manufacturing minutes

80A + 100Z ≤ 2000*60 Assembly minutes

1A ≥ 200 Model A minimum frames required.

A, Z ≥ 0 Non-negativity constraints

What are the optimal solution and the total profit contribution? (use Solver to find solution)
Another supplier offered to provide Kito Industries with an additional 200 pounds of the steel alloy at $2 per pound. Should Kito purchase the additional pounds of the steel alloy? Explain.
Kito is considering using upto 500 hours of overtime at $10 per hour to increase the available assembly time. What would you advise Kito to do regarding this option? Explain.

Because of increased competition, Kito is considering reducing the price of model A such that the new contribution to profit is $150 per unit. How would this change in price affect the optimal solution? Explain.
If the available manufacturing time is increased by 500 hours, will the shadow price for the manufacturing time constraint change? Explain.

Soupier Struck is a small food truck that sells soups near the UIW campus. Souper Struck offers two varieties of soups for their lunch special – Loaded Potato Soup and the Spicy Potato soup. At the beginning of the day, Souper Struck needs to decide how much of each soup to make. It is important to note that the truck always sells out of whatever they make due to their cleanliness, prices, and the proximity to a large university campus. The profit on one serving of the Loaded Potato Soup is $0.50 and on one serving of the Spicy Potato Soup is $0.60. Each serving of Loaded Potato requires 8 ounces of chicken broth, 3 tablespoons of potato flakes, 5 ounces of secret flavor mix. Each serving of Spicy Potato requires 6 ounces of chicken broth, 2 tablespoons of potato flakes, 4 ounces of secret flavor mix, and 4 ounces of special spicy sauce. Today, Souper Stuck has 3200 ounces of chicken broth, 1200 tablespoons of potato flakes, 2000 ounces of secret flavor mix, and 600 ounces of special spicy sauce on hand.

Develop an LP model that will tell Souper Stuck how many servings of Loaded Potato and Spicy Potato to make in order to maximize his profit today.

Find an optimal solution.

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Related Services

For the same problem as Q.2. regarding Souper Struck respond to the following
1. What is the shadow price for special sauce? Interpret it.
2. Increase the amount of special sauce available by 10 ounces and re-solve. Does the solution confirm the answer to part (a)? Give the new solution.

Premier Insights, Inc. has two consultants, Kristi and James, who can be scheduled to work for clients up to a maximum of 160 hours each, over the next month. A third consultant and the owner of the company, Brandon, has some administrative assignments already planned and is available for clients up to a maximum of 100 hours over the next month. The company has four clients with projects in process. The estimated hourly requirements for each of the clients over the four-week period are as follows:

Client Requested Hours

A 150

B 85

C 100

D 85

Hourly rates vary for the consultant–client combination and are based on several factors, including project type and the consultant’s experience. The rates (dollars per hour) for each consultant–client combination are as follows

Client

Consultant A B C D

Kristi 100 135 115 125

James 100 125 105 120

Brandon 200 175 150 140

Develop a network representation of the problem.
Formulate the problem as a linear program, with the optimal solution providing the hours each consultant should be scheduled for each client to maximize the consulting firm’s billings. What is the schedule and what is the total billing?

Premier Insights, Inc (from Q.4.) learns about some new requirements sent in by the clients which indicate that James doesn’t have the experience to be scheduled for client D. If this consulting assignment is not permitted, what impact does it have on total billings? What is the revised schedule? Re-formulate the LP and present the solution.

Advanced LP Applications

The Fireside Credit Union is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows

Type of loan/investment Annual Rate of Return (%)

Automobile loans 10

Furniture loans 12

Mortgage loans 5

Other Secured loans 15

Risk-free securities 5

Fireside will have $2.5 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments.

Automobile, furniture and other secured loans may not exceed the amount invested in Mortgage loans
Furniture and automobile loans together may not exceed the amount invested in risk-free securities
Other Secured loans may not exceed 12% of the funds invested in all other types of loans (automobile, furniture, and mortgage).
Risk-free securities may not exceed 20% of the total funds available for investment.

How should the $2.5 million be allocated to each of the loan/investment alternatives to maximize total annual return? What is the projected total annual return? Write a linear program and use Excel Solver to find the solution.

Product code: Operation Management-QA69

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