Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · medium
A company's total cost function is C(x)=0.02x2+30x+5000, and its price function is p(x)=150-0.04x (both in pesos, x = units). Find the number of units that maximizes profit.
- 1000 units
- 1500 units
- 2000 units
- 500 units
Answer
A. 1000 units
Solution
Profit P(x)=xp(x)-C(x)=x(150-0.04x)-(0.02x2+30x+5000)=120x-0.06x2-5000. P'(x)=120-0.12x=0 x=1000.
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