Answer :

Let number of automobiles produces be x and let the number of trucks


Produced be y.


Let Z be the profit function to be maximized.


Z = 2000x + 30000y


The constraints are on the man hours worked


Shop A 2x + 5y ≤ 180 (i) assembly


Shop B 3x + 3y ≤ 135 (ii) finishing


x, y ≥ 0


Corner points can ve obtained from


2x = 3y + 5y = 180 x = 0; y = 36 and x = 90; y = 0


3x + 3y ≤ 135 x = 0; y = 45 and x = 45; y = 0


Solving (i) and (ii) gives x = 15 and y = 30



Thus 0 automobiles and 36 trucks give max. profit of Rs 10, 80, 000/ -


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