Case 1:
Mustafa manages a manufacturing plant that produces two kinds of cricket bats: soft ball bats and hard ball bats. Business is good and no matter how many he produces, he can sell all of them. Both of the products are produced on the same machines but cost and price of both products are different. Now, he has to decide how many of each product should he produce to maximize the profits.
Question:
Which technique of decision making can help him in deciding the quantity of each product to be produced?
Support your answer with appropriate rationale.
Case 2:
Ali is a Project Manager of a construction firm. He has been assigned a project to build 3 conference halls for a client. Capacity of each hall should be at least 50 people and all of the halls should be completed within 40 weeks without incurring excessive costs. He is planning to meet the challenge of completing the project on time. He has identified various activities involved in the project and their sequence along with expected time required to complete each activity given in the following table:
Analyze the given information and decide which planning tool can help him to achieve the objective? Give appropriate reasoning to support your answer.
Idea Solution
Linear Programming 
Example
Consider a bicycle manufacturer that manufactures mountain bikes and street bikes, each of which generates a different profit level. The manufacturer would like to know how many bikes of each category to produce so as to maximize profits, given that the business can sell its entire output. Two different teams produce the mountain bikes and the street bikes by hand, each with production constraints in terms of how many bikes it can produce per day. The bikes also have to go through a machine finishing process that has a limited processing capacity. The business could use the linear programming technique to solve this sort of problem.
Linear program ming intro
Linear programming is constrain ed optimization , where the con straints and the objective function are all
linear. It is called “programming” because the goal of the calculations help you choose a “program” of
action .
Classic application:
1. Manufacturing — product choice
Several alternative outputs with different input requirements
Scarce inputs
Maximize profit