Question

5. Anthony owns a business that sells parts for electronic game systems. The profit for his business can be

modeled by the equation P = -0.2x2 + 10x – 25, where x is the quantity sold, in thousands, and P is the
profit in thousands
a) What is the maximum profit Anthony will receive
b) How many parts would he need to sell to receive the maximum profit?

Answer 1

Solution given:

p(x)=0

-0.2x2 + 10x – 25=0

-0.2(x²-50x+125)=0

x²-2.25.x+25²=25²-125

(x-25)²=500

x-25=
`√(500)`

x-25=±10√5

taking positive

x=22.3606+25

x=47.3606

taking negative

x= -22.3606+25

x=2.639

so

maximum profit Anthony will receive :47.3606*1000= 47360600(approach)

now

47360 .6 or 2639 parts he would need to sell to receive the maximum profit