Quadratic Equations

Question

For a certain company, the cost for producing x items is 35x+300 and the revenue for selling x items is 75x−0.5x2.

Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

 

Part b: Find two values of x  that will create a profit of $300.

Part c: Is it possible for the company to make a profit of $15,000?

Answer 1

Profit = R -C =35x +300 -(75x -.5x^2)

Profit = 300 -40x +(x^2)/2

300 profit when x = 0 and when

.5x^2 -40x = 0 = x(.5x -40)

.5x = 40

x = 80

15000 = 300 -40x +.5x^2

.5x^2 -40x -14700 = 0

discriminant is positive so yes, it can be done

x^2 -8x= 2940

x^2 -8x+ 16 = 2956

(x-4)^2 = 2956

x = 4 +/-sqr2956 = about 57 output gives profit of $15,000

this problem is not very realistic

no limit to profits

and positive profit when selling nothing