A workshop manufactures two products

MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

A workshop manufactures two products,

A

and

B

. Each unit of product

A

requires

2

hours of machine time and

1

hour of skilled labour, while each unit of product

B

requires

1

hour of machine time and

2

hours of skilled labour. Weekly availability is limited to

40

hours of machine time and

36

hours of skilled labour. The management also decides that the combined weekly output must be at least

m

units, where

m

is a non-negative integer determined by market demand. (i) Taking

x

and

y

to denote the weekly numbers of units of

A

and

B

respectively, write all the linear inequalities that express the above restrictions. (ii) For

m = 18

, sketch the region consisting of all feasible production plans and state whether it is bounded or unbounded. (iii) Find the range of values of

m

for which at least one feasible production plan exists. Explain your reasoning clearly.