For Incap T-shirts, the cost of producing x t-shirts can be expressed as C=0.6x2+0.52x+3200. The revenue they gain can be expressed as R=100x. What is the maximum profit (revenue subtract cost) they can make? In other words, what is the maximum value of R−C? Express your answer to 2 significant figures.

Remark

What is messing you up is the definition of a, b and c.

The general equation for a quadratic is

y = ax^2 + bx + c

a is the number in front of x^2. You seem to understand that.

b is the number in front of x.

c is the number that has no x associated with it.

Step One

Find ac

a = 1 ; c= 14. ac = 1*14 =14

Step Two

1 * 14 = c 1 + 14 = 15. That is not the value for b. The only other two you can try is 2 and 7

2 * 7 = 14 2 + 7 = 9 which does equal b. To put it in the terms of the question 2 + 7 = b = 9

Step 3

x^2 + 2x + 7x + 14

Step 4

1(x^2 + 2x) + 1(7x + 14)

x(x + 2) + 7(x + 2)

Step 5

The gcf is (x + 2) Pull it out as a common factor.

(x + 2)(x +7)