Question

The cost of manufacturing soccer balls is given by C=24,000+7x.

a) What is the slope of this equation and what does it represent?
b) What is the y-intercept of this equation and what does it represent?
c) If a manufacturer wanted to spend less than $30,000, what is the maximum number of balls that can be produced?

Options:
A. x≤ 30,000−24,000/7
B. x≥ 30,000−24,000/7
C. None of the
D. Both a and b

Answer 1

a) The slope of the equation represents the rate of change of the manufacturing cost with respect to the number of soccer balls produced. b) The y-intercept represents the manufacturing cost when no balls are produced. c) The maximum number of balls that can be produced for a cost less than $30,000 is x ≤ 30,000 - 24,000/7.

Step-by-step explanation:

a) The slope of the equation C = 24,000 + 7x is 7. The slope represents the rate of change of the cost of manufacturing soccer balls with respect to the number of soccer balls produced.

b) The y-intercept of the equation is 24,000. The y-intercept represents the cost of manufacturing soccer balls when no balls are produced (x = 0).

c) To find the maximum number of balls that can be produced for a cost less than $30,000, we need to solve the equation C = 30,000. Substituting this value into the equation C = 24,000 + 7x and solving for x, we get x = (30,000 - 24,000)/7. Therefore, the maximum number of balls that can be produced is x ≤ 30,000 - 24,000/7.