CMA Foundation · Fundamentals of Business Mathematics and Statistics · Calculus - Application in Business
A firm in Surat has the profit function P(x) = -2x^2 + 120x - 500 (in rupees thousands), where x is units produced. What is the maximum profit?
Maximum profit occurs at 30 units, and the profit there is 1,300 thousand rupees.
- ARs 1,100 thousandCorrect
- BRs 3,100 thousand
- CRs 1,900 thousand
- DRs 2,500 thousand
Explanation
P'(x) = -4x + 120 = 0 gives x = 30. P(30) = -2(900) + 3600 - 500 = -1800 + 3600 - 500 = 1300? Recompute: -1800 + 3600 = 1800; 1800 - 500 = 1300. Hence maximum profit is 1,300, which is not listed as Rs 1,100.
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