Operations Research Answers

The crumb and Custard bakery makes cakes and pies. The main ingredients are flour and sugar. The following linear programming model has been developed for determining the number of cakes and pies (x1 and x2 to produce each day to maximize profit.

Max Z=x1 + 5x2

Subject to:

8x1+10x2< 25(flour, lb)

2x1+4x2< 16(sugar, lb)

x1< 5(demand for cakes)

x1,x2 >0

Solve this model using simplex method.

 Solve the following LPP:  

Minimize Z= 120x1+60x2 

Subject to:  

20x1+30x2>= 900  

40x1+30x2>=1200  

x1,x2>=0

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Birr 25000 and Birr 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Birr 70 lakhs and if his profit on the desktop model is Birr 4500 and on portable model is Birr 5000. (Find optimal Solution by simplex Model)

 The Super Discount store (open 24 hours a day, every day) sells 8-packs of paper towels, at the rate of approximately 420 packs per week. Because the towels are so bulky, the annual cost to carry them in inventory is estimated at $.50. The cost to place an order for more is $20 and it takes four days for an order to arrive.

a. Find the optimal order quantity.

b. What is the reorder point?

c. How often should an order be placed? 

Transportation problem

1 2 3 4

50 750 300 450

650 800 400 600

400 700 500 550

Demand 10 10 10 10

Supply 12 17 11

A person has $ 100 to spend on two goods X and Y whose respective prices are $3 and $5.

A. Draw the budget line.

B. What happens to the original budget line if the budget falls by 25%?

C. What happens to the original budget line if the price of X doubles?

D. What happens to the original budget line if the price of Y falls to $4?

ABC company manufactures and sells two products P1 and P2. Each unit of P1 requires two hours of machining and one hour of skilled labour. Each unit of P2 requires one hour of machining and two hours of labour. The machine capacity is limited to 650 man hours. Only 300 unit's of product P1 can be sold in the market. The per unit contribution from product P1 is Ksh. 80 and product P2 is Ksh. 120 . Formulate a linear programming model

Q2. A school organized a book fair and in this book fair a book seller is selling his books under the following rules:

There are three different packages available.

First package contains 2 Islamic books, 2 Science books and 2 Geography books, second package contains 2 Islamic books, 4 Science books and 1 Geography books and third package contains 3 Islamic books, 4 Science books and 5 Geography books. The book fair has a total of 250 Islamic books, 300 Science books, and 270 Geography books. First package makes a profit of Rs. 120, second package makes Rs.100 and third package makes Rs.270 per pack. 

How many packs should be made to maximize book fair profits?

What will the profit be?

10. A can of cat food, guaranteed by the manufacturer to contain at least 10 units of protein, 20 units of mineral matter, and 6 units of fat, consists of a mixture of four different ingredients. Ingredient A contains 10 units of protein, 2 units of mineral matter, and 1 2 unit of fat per 100g. Ingredient B contains 1 unit of protein, 40 units of mineral matter, and 3 units of fat per 100g. Ingredient C contains 1 unit of protein, 1 unit of mineral matter, and 6 units of fat per 100g. Ingredient D contains 5 units of protein, 10 units of mineral matter, and 3 units of fat per 100g. The cost of each ingredient is Birr 3, Birr 2, Birr 1, and Birr 4 per 100g, respectively. How many grams of each should be used to minimize the cost of the cat food, while still meeting the guaranteed composition? (Hint: Solve through simplex model)