Question

The manufacturer of an energy drink spends $1.20 to make each drink and sells them for $2. The manufacturer also has fixed costs each month of $8,000.

a. Find the cost function C when x energy drinks are manufactured.
b. Find the revenue function R when x drinks are sold.
c. Show the break-even point by graphing both the Revenue and Cost functions on the same grid.
d. Find the break-even point. Interpret what the breakeven point means.

Answer 1

In order to find the cost function, revenue function, break-even point and its interpretation, we need to analyze the given information step by step.

Step-by-step explanation:

a. The cost function C when x energy drinks are manufactured is given by the equation C(x) = 1.20x + 8,000, where x is the number of drinks manufactured.

b. The revenue function R when x drinks are sold is given by the equation R(x) = 2x.

c. To show the break-even point, graph both the Revenue and Cost functions on the same grid. The break-even point is the point at which the revenue and cost are equal.

d. To find the break-even point, set the revenue equal to the cost and solve for x. In this case, 2x = 1.20x + 8,000. Simplifying the equation gives x = 8,000/0.80 = 10,000.

The break-even point means that the manufacturer needs to sell 10,000 energy drinks in order to cover all costs and not make a profit or loss.