Operations Research Answers

A pharmacy has determined that a healthy person should receive 70 units of proteins, 100 units of carbohydrates and 20 units of fat daily. If the store carries the six types of health food with their ingredients as shown in the table below, what blend of foods satisfies the requirements at minimum cost to the pharmacy? Make a mathematical model for the given problem

Foods Protein units Carbohydrates units Fat units Cost per unit

A 20 50 4 2

B 30 30 9 3

C 40 20 11 5

D 40 25 10 6

E 45 50 9 8

F 30 20 10 8

A farmer has 10 acres to plant in rice and corn. He has to plant at least 7 acres. However, he has only PhP1200 to spend and each acre of rice costs PhP200 to plant and each acre of corn costs PhP100 to plant. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of rice and 2 hours to plant an acre of corn. If the profit is PhP500 per acre of rice and PhP300 per acre of corn, how many acres of each should be planted to maximize profits?

A trust fund is planning to invest up to PhP6000 in two types of bonds: A and B. Bond A is safer than bond B and carries a dividend of 8 percent, and bond B carries a dividend of 10 percent. Suppose that the fund's rules state that no more than PhP4000 may be invested in bond B, while at least PhP1500 must be invested in bond A. How much should be invested in each type of bond to maximize the fund's return?

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A manufacturer produces two different models -x and y of the same product.Model x makes contribution of Rs 50 per unit and model y Rs 30 per unit towards total profit.Raw materials r1 and r2 are required for production.At least 18kg of r1 and 12kg of r2 must be used daily.Also at most 34hours of labour are to be utilised.A quantity of 2kg of r1 is needed for model x and 1kg of r1 for model y.For each of X and Y 1kg of r2 is required.It takes 3 hours to manufacture model x and 2hrs to manufacture y. How many units should be produced to maximise the profit?

Consider the following transportation problem:

To/From Store 1 Store 2 Store 3 Store 4 Supply_

Plant 1 19 30 50 10 7

Plant 2 70 30 40 60 9

Plant 3 40 8 70 20 18

Demand 5 8 7 14 34

Required:

i. Set Up The Transportation Tableau For This Problem And Determine

The InitialSolution

Using The Minimum Cell Cost Method.

ii. Solve Using MODI

iii. Formulate This Problem As A Linear Programming Model

Consider the following transportation problem:

To/From Store 1 Store 2 Store 3 Store 4 Supply

Plant 1 19 30 50 10 7

Plant 2 70 30 40 60 9

Plant 3 40 8 70 20 18

Demand 5 8 7 14 34

Required:

i. Set Up The Transportation Tableau For This Problem And Determine The InitialSolution

Using The Minimum Cell Cost Method.

ii. Solve Using MODI

iii. Formulate This Problem As A Linear Programming Model

A transportation problem involves the following costs, supply, and demand.

To

From 1 2 3 4 Supply

1 $500 750 300 450 12

2 650 800 400 600 17

3 400 700 500 550 11

Demand 10 10 10 10

Required:

i. Find the initial solution using the northwest corner method, the minimum cell cost

method, and Vogel's Approximation Method. Compute total cost for each.

ii. Using the VAM initial solution, find the optimal solution using the modified distribution

method (MODI).

A company produces 2 types of hats .Each hat of the 1 type requires twice as much as labour time as the 11 types. The company can produce a total of 500 hats a day. the market limits daily sales of 1 and 2 types to 150 and 250 hats .Assuming that the profit per hat are Rs.8 for types A and Rs 5 for type B.Formulate a LPP models in order to determine the number of hats to be produced of each type so as to maximize the profit