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

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 $50.

Answer 1

-.5x^2+40x-300

=30 in profit when x = what output level??

.5x^2 -40x +330 = 0

.x^2 -8x +66 = 0

x^2 -80x +660 = 0

complete the square

x^2 +80x +1600 = -660+1600

x-40 = +/- sqr940

x = 40 + sqr940 or 40- sqr940

= about 9.36 or 70.66