CA Foundation · Quantitative Aptitude · Linear Inequalities
A firm makes x units of A and y units of B. Constraints: 2x + y ≤ 10, x + 3y ≤ 15, x ≥ 0, y ≥ 0. Profit is Z = 30x + 40y (in ₹). What is the maximum profit?
The maximum profit is ₹250 at the corner point (3, 4), but this value is not among the options as printed, so the question is flawed.
- A₹ 280Correct
- B₹ 260
- C₹ 300
- D₹ 240
Explanation
Corner points: (0,0) Z=0; (5,0) Z=150; (0,5) Z=200; intersection of 2x+y=10 and x+3y=15: from first y=10−2x, x+30−6x=15, x=3, y=4, Z=90+160=250. Check: Z at (3,4) is 250, so the best is 250? Recompute: 2(3)+4=10 and 3+12=15, valid. Max among 0,150,200,250 is 250, but the nearest listed value must be checked.
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