Question

10) A company estimates that its weekly profit, P, in thousands of dollars, can be approximated by the formula P = -2x2 + 3x + 6, where x is the number of items produced per month in ten thousands. (Hint TI 84 Plus)
a) How many items should the company produce per week to earn the maximum profit?
b) Find the maximum weekly profit?

Answer 1

@eliassaab

Answer 2

i just need help on this

Answer 3

Let
\[\large
u=\frac x 4\\

P(u) = -\frac{u^2}{8}+\frac{3 u}{4}+6=\\
6-\frac{1}{8} \left(u^2-6
u\right)=\\6-\frac{1}{8} \left(u^2-6
u+9-9\right)=\\-\frac{1}{8}
(u-3)^2+\frac{9}{8}+6=\\\frac{57}{8}-
\frac{1}{8} (u-3)^2


\]
The maximum is attained when u=3 and this maximum is \(\large \frac {57}8\)

Answer 4

One has to sell 3(10,000)=30,000 items in a week
the maximum profit is
\[
\frac {57}8 \times 10000=$71,250
\]