Problem solving and business applications

Question

The cost and revenue functions for producing and selling x units of a product are given. Cost and revenue are expressed in dollars.

C(x)=30,020 + 16x

R(x)=36x

a. Find the number of units that must be produced and sold to break even. At this level, what is the dollar amount coming in and going out?

b. Write the profit function from producing and selling x units of the product.

Answer 1

As Peter said "break even" is when revenue is equal to cost so you set the equations equal and solve for x. Your x value is telling you the number of units that are sold. So in order to find the dollar amount coming in (revenue) or going out (cost) you will need to plug in your x value into either the revenue or cost equation to find the dollar amount of x units.

For b the profit is found by taking the revenue and subtracting the costs. So take the revenue equation and subtract the cost equation from it. Remember to subtract both 30,020 and 16x; distribute your minus sign(-30,020-16x). The resulting equation will be the profit equation.