This problem explores your understanding of revenue, cost and profit. This problem is similar to Problem 3 on the Midterm and Problem 3 on the Midterm Study Guide.

**Problem 11** The cost of producing x t-shirts is C(x) dollars where. A t-shirt sells for $16 each. Complete the parts below by solving appropriate equations algebraically or graphically and document the steps you follow.

a. Find the break-even quantity.

**Solution** The revenue function is *R*(*x*) = 16*x*. To find the break-even point set *R*(*x*) = *C*(*x*) and solve for *x*.

b. What profit will the company receive if it sells 2000 t-shirts?

**Solution** The profit function is the difference between revenue *R*(*x*) and cost *C*(*x*),

c. How many shirts will produce a profit of $20,000?

**Solution** Set the profit function equal to 20,000 and solve for x: