Question

If the demand curve for a particular commodity is p = −0.09x + 51 and the total cost function C(x) = 1.32x2 + 11.7x+ 101.4,where x is the level of production: Find (a) The revenue R(x) and profit Π(x). How much will have been spent on production by the end of the third hour? When will the total manufacturing cost reach $11,000?

Answer 1

a. Revenue R(x)= P*x= -0.09x^2+51x

Profit π(x)= Revenue - Cost=R(x)- C(x)

π(x)= -0.09x^2+51x-1.32x^2- 11.7x-101.4

π(x)= -1.41x^2+39.3x-101.4

C(x)= 11000= 1.32x^2+11.7x+101.4

0= 1.32x^2+11.7x-10898.6

Solving for positive value of x,

we get x=86.5

When production =86.5, manufacturing cost reach $11000