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.
Let x units of product A and y units of product B be produced.
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.
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.
\[0 \leq x \leq 7000, 0 \leq y \leq 10000\]
Total profit = \[60x + 40y\]
Here, we need to maximize profit
Thus, the objective function will be maximize
\[Z = 60x + 40y\]
Hence, the required LPP is as follows:
Maximize Z = 60x + 40y
\[5x + 3y \leq 45000\]
\[x \leq 7000\]
\[y \leq 10000\]
\[x, y \geq 0\]
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