Operations Research Answers

The Colonial pottery company produces two products daily – bowls and mugs. The Company has limited amounts of resources used in the production of these products – clay and labor. For the bowl, it would require 1 hr of labor and 4 lb. of clay to produce while the mug requires 4 lb of clay and 2 hrs of labor to produce. The items are sold at $4/unit for the bowl while $5/unit for the mug. There are 40 hrs of labor and 120 lbs. of clay available each day for production. What should be the optimal number of products to have maximum profit?

(c) 

The forecast of a product for the first week of March was 200 units, whereas the actual 

demand turned out to be 220 units. 

i. 

Find the forecast for the second week of March by assuming the smoothing constant 

( ) α

as 0.35.      

ii. 

Find the forecast for the third week of March if the actual demand of the second 

week is 210 units.     

Use simplex method to maximize 𝑓 = 3𝑥 + 5𝑦 + 4𝑧 subject to the conditions 2𝑥 + 3𝑦 ≤ 18 2𝑥 + 5𝑦 ≤ 10 3𝑥 + 2𝑦 + 4𝑧 ≤ 15 and 𝑥, 𝑦, 𝑧 ≥ 0.

Use simplex method to maximize 𝑓 = 3𝑥 + 5𝑦 + 4𝑧 subject to the conditions 2𝑥 + 3𝑦 ≤ 18 2𝑥 + 5𝑦 ≤ 10 3𝑥 + 2𝑦 + 4𝑧 ≤ 15 and 𝑥, 𝑦, 𝑧 ≥ 0. 

Solve the following problem by simplex method and check for alternative solution. If possible,

find the alternative solution also. Does this problem has infinite number of solutions ?

Maximize Z = 4x₁ + 10x₂

Subject to

2x₁ + x₂ ≤ 10

2x₁+ 5x₂ ≤ 20

2x₁ + 3x₂ ≤ 18

where x₁, x₂ are unrestricted in sign.

Consider the following LPP

Maximize Z = 2x₁ + 3x₂

Subject to

x₁ + 3x₂ ≤ 6

3x₁ + 2x₂ ≤ 6

x₁, x₂ ≥ 0

a. Determine all the basic solutions of the problem, and classify them as feasible and

infeasible.

b. Carry out the full tableau implementation of the simplex method, starting with the basic

feasible solution (x₁, x₂) = (0, 0)

Consider the set of equations

5x₁ − 4x₂ + 3x₃ + x₄ = 3

2x₁ + x₂ + 5x₃ − 3x₄ = 0

x₁ + 6x₂ − 4x₃ + 2x₄ = 15

where x₁ = 1, x₂ = 2, x₃ = 1, x₄ = 3 is a feasible solution. Is this solution feasible solution

If not, reduce this feasible solution to two different basic feasible solution.

2. A manufacturer produces two models of a certain product: model A and model B. There is a R20 profit on model A and an R35 profit on model B. Three machines M1,M2 and M3 are used jointly to manufacture these models. The number of hours that each machine operates to produce 1 unit of each model is given in the table: Model A Model B Machine M1 1 1 2 1 Machine M2 3 4 1 1 2 Machine M3 1 1 3 1 1 3 No machine is in operation more than 12 hours per day. Now let x be the number of model A made per day and y be the be the number of model B made per day. Then x and y satisfies the following constrains

Problem 3: Kebede & co. is considering investing some money that they inherited.

The following payoff table gives the profits that would be realized during the next

year for each of three investment alternatives the co. is considering:

a) What decision should be done by Maximax?

b) What decision should be done by Maximin?

c) What decision should be done by Criterion of realism? Assume that

coefficient of realism, α, to be 0.80.

d) What decision should be done by Equally likely?

e) What decision should be done by Minimax regret?

f) What decision should be done by EMV?