Question

Exel solver

SOLVER EXCEL EXAMPLE Turley Tailor Inc. makes shirts and coats A shirt requires 1 hour of cutting and 5 hours of sewing. A coat requires 4 hours of cutting and 3 hours of sewing. There are a maximum of 28 hours of labor in the cutting department each day and 55 hours in the sewing department. The maximum number of coats that can be produced is two more than the number of shirts. A shirt costs $1 to produce. A coat costs $2 to produce. The minimum production cost is $4 Each shirt produces $26 in profit and each coat $57 in profit. Find the number of shirts and coats to produce the maximum profit. What is this maximum profit?

Answer 1

This question is based on linear programming concept.

It is given that to produce a shirt, i.e. output X, requires 1 hour of cutting and 5 hours of sewing.

Similarly, output y(coat) requires 4 hour of cutting and 3 hours of sewing.

Total available inputs, i.e. hour of cutting and hour of sewing are 28 and 55 respectively.

Producer makes a profit of Rs.26 on each unit of X and Rs.57 on each unit of y.

This can be better understood by presenting the given information in tabular form:

Input	product x(shirt)	product y (coat)	total inputs available
Labour of cutting	4	4	28
Labour of sewing	5	3	55
Profit	26	57

It is also given that maximum number of coats can be produced is two more than number of shirts, i.e. y= X+2.

According to question, we have to maximize profit:

Maximise Profit: P= 26x + 57y

Subject to a) 4x +4y=28 i.e. x+y =7

or 5x + 3y= 55

b) y=X+2

By solving equations: x+y=7 & y=x+2, we get X=2.5 & y = 4.5

Similarly, solve 5x+3y=55 & y=X+2, we get X= 6.12 & y = 8.12

To maximize the profit, we have to solve the equations x+y= 7 & 5x+ 3y=55, we get X=12 & y=14.

By substituting all the values of x & y in profit function, we can check, when the profit is get maximised.

P= 26x + 57y

At ( x=2.5, y=4.5) P = 26(2.5) + 57(4.5)= 321.5

At (X=6.12, y=8.12) P= 26(6.12)+57(8.12) = 621.96

At (X=12, y= 14) P= 26(12)+57(14)= 1110

A producer earns a maximum profit =1110 by producing 12 shirts and 14 coats.