Question

A company sells two different products A and B. The two products are produced in a common production process and are sold in two different markets. The production process has a total capacity of 45000 man-hours. It takes 5 hours to produce a unit of A and 3 hours to produce a unit of B. The market has been surveyed and company officials feel that the maximum number of units of A that can be sold is 7000 and that of B is 10,000. If the profit is Rs 60 per unit for the product A and Rs 40 per unit for the product B, how many units of each product should be sold to maximize profit? Formulate the problem as LPP.

Answer 1

Let x units of product A and y units of product B be produced.
Then,
Since, it takes 5 hours to produce a unit of A and 3 hours to produce a unit of B.
Therefore, it will take 5x hours to produce x units of A and 3y hours to produce y units of B.
As, the total capacity is of 45000 man hours.
$\Rightarrow 5x+3y\le 45000$
Also,
The maximum number of units of A that can be sold is 7000 and that of B is 10,000 and number of units cannot be negative.
Thus, $0\le x\le 7000,0\le y\le 10000$
Now,
Total profit = $60x+40y$
Here, we need to maximize profit

Thus, the objective function will be maximize $\mathrm{Z}=60x+40y$

​Hence, the required LPP is as follows:

Maximize Z = 60x + 40y

subject to

$$\begin{gathered} 5x+3y\le 45000 \\ x\le 7000 \\ y\le 10000 \\ x,y\ge 0 \end{gathered}$$