P'(x)=10^6(e^0.001x)(0.001x+0.999)
Since P'>0 for all x>0, P is increasing; the maximum profit is found at the rightmost end of the interval.
The net monthly profit, in dollars, from the sale of a certain item is given by the formula P(x) = 10^6[1 + (x-1)e^0.001x], where x is the number of items sold.
a) Find the number of items that yield the maximum profit. At full capacity,
the factory can produce 2000 items per month.
b) Repeat part a, assuming that, at most, 500 items can be produced per
month.
1 answer
1 answer