Question

Annual profit in thousands of dollars is given by the function, P(x) = -.01x2 + 50x + 30,000, where x is the number of items sold, x ≥ 0.

will this profit function have a maximum? if so what would it be?

Answer 1

would i use the formula x=-b/2a

Answer 2

you can derive it to get the maximum

y'=-.02x+50

try getting the critical points

-.02x + 50 = 0

50=.02x
x= 2500

get the y

y= -.01(2500)^2 + 50(2500)+30000
y= -62500 + 125000 + 30000
y= 92500

the function has a maximum 92500 at x = 2500

Answer 3

that is what i got

Answer 4

so the max weekly profit is approx 92,500 when 2,500 units are sold

Answer 5

yes ^^

Answer 6

so then what steps should the company do to prepare for my answer which was 92,500 was the max weekly profit when 2,500 units are sold?

Answer 7

can someone help me with this one question?