A laptop company has discovered their cost and revenue functions for each day: c(x) = 3x2 − 10x + 200 and r(x) = −2x2 + 100x + 5
0. if they want to make a profit, what is the range of laptops per day that they should produce? round to the nearest number which would generate profit.
Given that: c(x) = 3x2 − 10x + 200<span> and r(x)=</span><span>−2x2 + 100x + 50
Profit is given by: P(x)=r(x)-c(x)
P(x)=(</span>−2x2 + 100x + 50)-(3x2 − 10x + 200) P(x)=-5x^2+110x-150 thus: at maximum profit P'(x)=0 thus: P'(x)=-10x+110=0 hence: x=11 thus the number of units required for one to make profit is 11 units
