Final Exam Study Guide Problem 11 Solution

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) = 16x. To find the break-even point set R(x) = C(x) and solve for x.

final_study_guide_soln_11a

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),

final_study_guide_soln_11b

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

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

final_study_guide_soln_11c