Models P and Q earn profits of Rs. 100 and Rs. 80 per piece and take 5 and 3 hours to produce. Available time is 150 hours and total batch size is 40. To maximize profit, how many P units should be produced?
Let $x$ units be P, leaving $40-x$ units of Q. The time constraint is $5x+3(40-x)\leq150$, giving $x\leq15$. Profit is $100x+80(40-x)=3200+20x$, which increases with x. Therefore choose the largest feasible value $x=15$; Q production is 25 units and all 150 hours are used.
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