Operations Research Answers

A Manufacturer produces two products, the Klunk and the Klick. Klunk has a contribution

to profit of $3, and the Klick $4 per unit. The manufacturer wishes to establish the weekly

production plan that maximizes profit. Production of these products is limited to machine,

labor and material constraints. Each Klunk requires four hours machining, four hours labor

and one kilogram of material, where as each Klick requires two hours machining, six hours

labor and one kilogram of material. Machining and labor has a maximum of one hundred

and one hundred and eighty hours available, and total material available is forty kilograms.

Because of a trade agreement, sales of Klunk are limited to a weekly maximum of twenty

units and to honor an agreement with an old established customer at least ten units of Klick

must be sold each week.

i. Determine graphically using linear programming a suitable production mix of Klunk

and Klick. [12]

ii. What will be the company’s maximum profit?

What and define PERT

What and define CPM

At the start of the current week there are 30 units of X and 90 units of Y in stock. Available processing time on machine A is forecast to be 40 hours and on machine B is forecast to be 35 hours. The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units. Company policy is to maximize the combined sum of the units of X and the units of Y in stock at the end of the week.

 Formulate the problem of deciding how much of each product to make in the current week as a linear program.

 Solve this linear program graphically.

Grain Handlers Limited has three warehouses, W1, W2 and W3. The table below shows the inventories of rice in the three warehouses.

Warehouse                    W1    W2    W3

Inventory (bags)           260    168    172

The company is required to supply three of its companies C1, C2, and C3 with rice. The requirements of the customers are as follows:

Customer                       C1     C2     C3

Requirement (bags)     280    120    200

The data below shows the cost of transporting one bag of rice from the warehouse to the customers

Transportation cost per bag (sh)

Customer

C1

C2

C3

W1

100

80

120

Warehouse

W2

140

80

140

W3

160

120

140

Required

The optimum solution

Coal is mined and processed at the following four mines in Kentucky, West Virginia, and Virginia:

Location Capacity (tons)

A. Cabin Creek 90

B. Surry 50

C. Old Fort 80

D. McCoy 60 ____

280

These mines supply the following amount of coal to utility power plants in three cities:

Plant Demand (tons)

1. Richmond 120

2. Winston-Salem 100

3. Durham 110 ____

330

The railroad shipping costs ($1,000s) per ton of coal are shown in the following table. Because of

railroad construction, shipments are now prohibited from Cabin Creek to Richmond:

To

From 1 23

A $ 7 $10 $ 5

B 12 9 4

C 7 3 11

D 9 57

a. Set up the transportation tableau for this problem, determine the initial solution using

VAM, and compute total cost.

b. Solve using MODI.

c. Are there multiple optimal solutions? Explain. If there are alternative solutions, identify them.

d. Formulate this problem as a linear programming model.

A retail store stocks two types of customized travel bags, A and B. The store can sell a maximum of 400 type of A bags and a maximum if 300 type B bags per week. However, the store can only store up to 600 bags of both types because of limited storage capacity. The store earnd the profit of 30 per type A bag and a profit of 50 per type B bag. How many of each type of bags should the store keep per week to maximize the profit?

State the two categories of inventory models

State four characteristics of 2-persons zero-sum game

World renowned ice cream entrepreneurs Sfiso and Richard produce two types of premium

dairy ice cream products, Sfiso n' Richard’s Chocolate Concussion and Vanilla Brain Freeze.

Their chocolate ice cream requires 6𝑙𝑙 milk and 8𝑙𝑙 of peanuts per litre while the vanilla option

requires 9𝑙𝑙 milk and 5𝑙𝑙 peanuts per litre. Sfiso and Richard currently enjoy a surplus of all

other ingredients required for their ice cream but only have 360𝑙𝑙 of milk and 400𝑙𝑙 of peanuts

for this limited production run. Given that the entrepreneurs charge 𝑅𝑅5 for each container of

Chocolate Concussion and 𝑅𝑅7 for each Vanilla Brain Freeze, how many of each type should

Sfiso and Richard produce in order to maximize their profit and what is the maximum?

Approximate your answer to the nearest tenth of a litre.