A workshop makes a profit of Rs. 40 on each unit of product A and Rs. 50 on each unit of product B, and it also pays a fixed cost of Rs. 500 a day whatever it makes. The corner points of the feasible region for the daily output (x units of A, y units of B) are (0, 0), (30, 0), (20, 15) and (0, 25). The maximum net profit in a day is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs. 1050
The net profit is the profit on the units less the fixed cost:
\(Z = 40x + 50y - 500\)
Values of Z at the corner points:
\(Z(0, 0) = -500\)
\(Z(30, 0) = 1200 - 500 = 700\)
\(Z(20, 15) = 800 + 750 - 500 = 1050\)
\(Z(0, 25) = 1250 - 500 = 750\)
The maximum net profit is Rs. 1050, at (20, 15). The constant 500 lowers every value equally, so it does not change the point of maximum.