An automobile manufacturer makes automobiles and trucks in a factory that is divided into two shops. Shop A, which performs the basic assembly operation must work 5 man-days on each truck but only 2 man-days on each automobile. Shop B, which performs finishing operations, must work 3 man-days for each automobile or truck that it produces. Because of men and machine limitations, shop A has 180 man-days per week available while shop B has 135 man-days per week. If the manufacturer makes a profit of Rs. 30000 on each truck and Rs. 2000 on each automobile, how many of each should he produce to maximize his profit?, Formulate this as a  LPP.

Explanation

Let x variety of trucks and y number of automobiles were created to maximize the profit.
Since, the manufacturer makes profit of Rs.`30000` on every truck and Rs.`2000` on every automobile.
`∴ On x `number of trucks and y number of automobiles profit would be Rs.`30000x` and Rs.`2000y` respectively.
Total profit `=Rs.(30000x+2000y)`
Let z denotes the total profit. Then,
`=>z=30000x+2000y`
Since, 5 man -days and 2 man-days were needed to provide every truck and automobile at shop A.
∴ 5x man-days and 2y man-days are required to produce each truck and y automobiles at shop A.
Also,

Since 3 man-days were required to produce each truck and automobile at shop B.
`∴ 3x` man-days and `3y` man-days are required to produce `x` trucks and `y` automobiles.

A, shop A has 180 man-days per week available while shop B has 135 man-days per week.

`∴ 5x+2y≤180, 3x+3y≤135`
Number of trucks an automobiles cannot be negative.
`∴ x,y≥0`
Hence, the specified LPP is as follows :
`text(Maximize)
z=30000x+2000y`
Subject to

`5x+2y≤180`,

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