Operations Research Answers

 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)

A trust fund is planning to invest up to P600,000 in

two type of bonds: A and B. Bond A carries a

dividend of 25% and B, 30%. Suppose the fund rules

state that no more than P400,000 may be invested in

bond B, while at least P150,000 must be invested in

bond A, how much should be invested in each type

of bond to maximize the fund’s return?

500 750 300 450 compute with north West corner method

A city has two subrubs subrub x anf subrub y over the past several years, the city has experienced a populatin shift from the city to the subrubs

{F} The furniture company inexpensive tables and chairs. The production process of each is similar in the painting department each table take 4 hours of carpentry and 2 hours in the painting department. Each chair requires 3 hours of carpentry and 1 hour painting department. During the current product period 240 hours of carpentry time are available and 100 hrs in the painting is available. Each table sold yields of profit of $7 and chair produced sold for $5 profit. Find the best combination of table and chairs to manufacture in order to reach the maximum number of profit?