Solve and show work in excel Linear Programming Applied Practice Solutions Probl

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Solve and show work in excel

Linear Programming Applied Practice Solutions Problem 1: Finance- Allocation of Funds Madison Finance has a total of $20 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 10% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to four times the total amount of automobile loans. Determine the total amount of loans of each type Madison should extend to each category in order to maximize its returns Problem 2: Manufacturing-Production Scheduling An acoustical company manufactures a CD storage cabinet that can be bought fully assembled or as a kit. Each cabinet is processed in the fabrications department and the assembly department. If the fabrication department only manufactures fully assembled cabinets, then it can produce 200 units/day; but if it only manufactures kits, then it can produce 300 units/day. Each fully assembled cabinet contributes $40 of profit, while each cabinet kit contributes $50 of profit. How many fully assembled units and how many kits should the company produce per day in order to maximize its profits? Problem 3: Nutrition-Diet Planning Suppose a person has decided to include brown rice and soybeans as part of his daily diet. The goal is to design the lowest-cost diet that provides certain minimum levels of protein, calories, and vitamin B2 (or riboflavin). One cup of uncooked brown rice costs 21 cents and contains 15 grams of protein, 810 calories, and 1/9 of a milligram of riboflavin. One cup of uncooked soy beans costs 14 cents and contains 22.5 grams of protein, 270 calories, and 1/3 of a milligram of riboflavin. If minimum daily requirements are 90 grams of protein, 1620 calories, and 1 milligram of riboflavin, design the lowest-cost diet meeting these specifications Problem 4: Manufacturing-Production Scheduling A company manufactures products A, B and C. Each product is processed in three departments:11, 11 and 111. The total available labor-hours per week for departments 1, 11, and 111 are 900, 1080, and 840, respectively. The time requirements (in hour per unit) and profit per unit for each product are as follow.s ProductProduct Product Dept. I Dept. II Dept. IIT Profit 2 2 2 2 $18 $12 $15

Explanation / Answer

Problem 1 - Maximize Returns (R) subject to constraints

Let home loan be X and auto loan be Y

So we are to maximize the objective function: R = 0.10X + 0.12Y

X+Y<= 20,000,000 (Less than or equal to 20MN)

X>= 4Y (more than or equal to 4Y)

X>= 0

Y>= 0

Eq 1 , X+Y = 20,00,000

If Y= 0, X = 20,000,000 (Condition 1)

If X = 0 , Y = 20,000,000 (Condition 2)

Eq 2, X = 4Y

if X = 0, Y= 0

Solving Eq 1 and Eq 2,

5Y = 20,000,000

Y = 4,000,000 , X = 16,000,000 (Condition 3)

Only two conditions satisfes constraint

1. If Y = 0, X = 20,000,000 , all constraints are satisfied.

2. If Y = 4,000,000 , X = 16,000,000 , all constraints are satisfied.

R 1 = 0.10X + 0.12Y = 0.10 * 20,000,000= 2,000,000

R 2 = 0.10X + 0.12Y =0.10 * 16, 000,000 + 0.12* 4,000,000 = 2,080,000

So we pick Condition 3 as our solution.

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