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A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry business. He provides you with data to help him optimize the sales. The data is that Old hens can be bought for K2 each but young one cost K5 each. The old hens lay 3 eggs per week and young ones 5 eggs per week, each egg being worth 30ngwee. A hen cost K1 per week to feed. If a person has only K80 to spend on hens, how many of each kind should he buy to get a profit of more than K6 per week assuming that he can’t house more than 20 hens?

A certain manufacturer produces two product P & q. Each unit of product P requires

(in its production) 20 units of row material A & 10 units of row material B. each unit of

product of requires 30 units of raw material A & 50 units of raw maternal B. there is a

limited supply of 1200 units of raw material A & 950 units of raw material B. How many

units of P & Q can be produced if we want to exhaust the supply of raw materials?

A branch of a bank has only one typist since the typing work varies in length the typing rate is randomly distributed approximating a poisson distribution with mean service rate at 8 letters per hour the letters arrive at a rate of 5 per hour during the entire 8 hours work day if the type writer is valued at 2 euros per hour determine

I) equipment utilization

Ii) percent that the arriving letter has to wait

Ii) average system time

iv) average cost due to waiting on the part of the typewriter

Maximize Z=80X1+120X2

Subject to X1+X2<9

20X1+50X2<360

X1>2

X2>3

X1+X2>0

Solve using simplex method

Minimize Z=10x1+12x2

Subject to:

40x1+30x2>=150

20x1+20x2>=90

10x1+30x2>=60

QUESTION THREE

A poultry farmer in Lufyanyama has obtained a loan from the Bank to boost his poultry

business. He provides you with data to help him optimize the sales. The data is that Old

hens can be bought for K2 each but young one cost K5 each. The old hens lay 3 eggs

per week and young ones 5 eggs per week, each egg being worth 30ngwee. A hen cost

K1 per week to feed. If a person has only K80 to spend on hens, how many of each kind

should he buy to get a profit of more than K6 per week assuming that he can’t house

more than 20 hens?

a)Formulate the problem as a linear programming model [8 Marks]

b)Using the graphical method procedure, how many hens should he buy of each kind to

maximize the profit per week? [10 Marks]

c) Determine the ranges of optimality for the objective function coefficients

A retired employee wants to invest no more than P 1,500,000.00 by buying stock from a well-known bank and a university. The stock from the bank offers 7% interest while the stock of a university pays a 5% return. He decided to invest no more than P 800,000.00 in the stock from the bank and at least P 300,000.00 in the stock of the university. Also, he wants his investment in the stock from the bank to be smaller than his investment in the stock of the university. How much stock should he buy for each investment to maximize his profit? Create an LP Model and solve using the graphic method.

1.Develop your own original LP problem with two constraints and two real variables.

(a) Explain the meaning of the numbers on the right-hand side of each of your constraints.

(b) Solve your problem graphically to find the optimal solution.

(c) Illustrate graphically the effect of increasing the contribution rate of your first variable by 50% over the value you first assigned it. Does this change the optimal solution?

A small firm manufactures and sells litre cartons of non-alcoholic cocktails, X and

Y, which sell for $1 and$1.25, respectively. Each is made by mixing fresh orange, pineapple, and apple juices in different proportions. X consists of one part orange, six parts pineapple and one part apple. Y consists of two parts orange, three parts pineapple and one part apple. The firm can buy up to 300 litres of orange juice, up to 1125 litres of pineapple juice and up to 195 litres of apple juice each week at a cost of $0.72,$0.64 and \$0.48 per litre, respectively. Find the number of cartons of X and Y that the firm should produce to maximise profits. You may assume that non-alcoholic cocktails are so popular that the firm can sell all that it produces.

3. A product is manufactured by four factories A, B, C and D. The unit production costs in them are ETB 2, ETB 3, ETB 1 and ETB 5 respectively. Their production capacities are 50, 70, 30 and 50 units respectively. These factories supply the product to four stories, demands of which are 25, 35, 105, and 20 units respectively. Unit transportation cost in ETB for each factory to each store is given in the table below.

Stores

1 2 3 4

2 4 6 11

10 8 7 5

13 3 9 12

4 6 8 3

A

Factories B

C

D

Determine the transportation plan to minimize the total production-cum-transportation cost by using:

a. Vogel’s Approximation Method (VAM) for initial basic feasible solution

b. Find the optimal solution using Modified Distribution Method (MODI) method

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