A firm produces two products and

MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

A firm produces two products

P

and

Q

. The production of one unit of

P

requires

2

kg of raw material R

_1

and

1

kg of raw material R

_2

. One unit of

Q

requires

1

kg of R

_1

and

2

kg of R

_2

. In a given week at most

12

kg of R

_1

and at most

10

kg of R

_2

are available. The contribution to profit is ₹ 5 per unit of

P

and ₹ 4 per unit of

Q

. Let

x

be the number of units of

P

and

y

the number of units of

Q

produced in that week. (a) Write all constraints on

x

and

y

, including non-negativity. (b) Draw the feasible region corresponding to the constraints in part (a). List the exact coordinates of every vertex. (c) Determine the values of

x

and

y

(not necessarily integers) that maximise the weekly profit and compute this maximum profit. (d) If the firm can only produce whole units of each product, find the integer-valued pair

(x,y)

that gives the highest profit and state that profit. Compare it with the profit obtained in part (c).

Related theory

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