Question

Question 1

Luluapple makes popular clothing. A few years ago Luluapple introduced a new line of shorts, pants, and shirts. Management wants to make the amount of each product so as to maximize profits. Each type of clothing is routed through two departments A and B. The relevant data for each product are as follows:

	Processing time (hours)
Product	Department A	Department B	Material (meters)
Shirts	2	1	2
Shorts	2	3	1
Pants	3	4	4

Department A has 120 hours of capacity, department B has 160 hours of capacity, and 90 meters of material are available. Each shirt contributes $10 to profits; each pair of shorts, $10; and each pair of pants, $23.

1. Formulate the problem algebraically a linear programming model for this problem. (5 marks)
2. Solve this problem using Excel. (5 marks)

Question 2

Crombie supermarket sells its private label brand of canned peas as well as other national brands. The store makes a profit of $0.28 per can for its private label peas and a profit of $0.19 for any of the other brands. The store has 6 square feet of shelf space available for canned peas, and each can of peas takes up 9 square inches of that space. Analytics show that each week the store sells less than half as many cans of its private label brand as it does the other national brands. The store wants to know how many cans of its own brand of peas and how many cans of the other brands to stock each week on the allocated shelf space in order to maximize profits.

1. Formulate the problem algebraically a linear programming model for this problem. (5 marks)
2. Solve this problem using Excel. (5 marks)

Question 3

The esteemed brokerage firm of Black, Scholes and Merton has just been instructed by one of its clients to invest $250,000 of her money obtained recently through the sale of Netflix, Inc. The client has a good deal of trust in the brokerage firm, but she also has her own ideas about the distribution of the funds being invested. In particular, she requests that the firm select whatever stocks and bonds they believe are well rated, but within the following guidelines:

1. Municipal bonds should constitute at least 20% of the investment
2. At least 40% of the funds should be placed in a combination of electronic firms, airline firms and drug manufacturers
3. No more than 50% of the amount invested in municipal bonds should be placed in a high risk, high yield nursing home stock.

Subject to these constraints, the client’s goal is to maximize projected return on investment. The firm of Black, Scholes and Merton, aware of these guidelines, prepare a list of high quality stocks and bonds and their corresponding rates of return:

Investment	Projected Rate of Return (%)
Bruderheim municipal bonds	5.3
SAMU Electronics	6.8
Westplane Airlines	4.9
Trudeau Drugs	8.4
Happy Days Nursing Homes	11.8

1. Formulate the problem algebraically a linear programming model for this problem. (5 marks)
2. Solve this problem using Excel. (5 marks)

Question 4

Professor Allister teaches two sections of finance and two sections of business statistics – what a lucky professor! Combined there are 160 final exams to be graded. Professor Allister has two graduate assistants, Steve and Megan, who will grade the final exams. There is a 3 day period between the time the exam is administered and when the final grades must be posted. During this period, Steve has 15 hours available and Megan has 15 hours available to grade the exams. It takes Steve an average of 7.2 minutes to grade an exam, and it takes Megan 12 minutes to grade an exam; however, Steve’s exams will have errors that require Professor Allister to ultimately regrade 10% of the exams, while only 6% of Megan’s exams will require regrading. Professor Allister wants to know how many exams to assign to each graduate assistant to grade in order to minimize the number of exams to regrade.

1. Formulate the problem algebraically a linear programming model for this problem. (5 marks)
2. Solve this problem using Excel. (5 marks)

Answer 1

1. Let X, Y & Z be the number of Shirts, Shorts & Pants manufactured respectively.

Our objective is to maximize the profit earned from selling this manufactures shirts, shorts and pants. Thus, our objective function is-

Max(10*X+10*Y+23*Z)

Our Constraints are-

From the processing hour capacity of Department A

2*X+2*Y+3*Z <= 120

From the processing hour capacity of Department B

1*X+3*Y+4*Z <= 160

From the material availability

2*X+1*Y+4*Z <= 90

As the Shirts, Shorts & Pants can't be manufactured in fractions and negatives-

X,Y,Z >= 0, with Integer Values

The Solver screenshots are-

Thus, they should manufacture 6 shirts, 38 shorts and 10 pants.

2. Let X be the quantity of Private Label peas stocked and Y be the quantity of National Label peas stocked

Our Objective is to maximize the profit from the sale of Private & National Label Peas. Thus our objective function is-

Max(0.28*X+0.19*Y)

We know 6 square foot = 864 square inch

Our Constraints would be-

From the space availability-

9*X+9*Y <= 864

From the Sale trend-

2*X <= Y

As the cans can't be in fractions and negative numbers-

X,Y >= 0, Integer Values only

The Solver screenshots are-

Thus, 32 cans of Private Label and 64 cans of National Label should be stocked

HOMEWORKLIB RULES prohibits Experts from answer more than 4 sub-questions in a single query. Please post the remaining questions as separate query.

Please Like & Provide your reviews in comments. :-)