1. Table of Contents Linear Inequalities: Application A company that manufactures compact discs has monthly fixed costs totaling $28,000. It also costs the company $0.50 to make each compact disc. If the compact discs are sold for $0.95 each, how many need to be made and sold each month (x) for the company to make a profit? To make a profit, the company's monthly revenue, R, (money it takes in for the sales) must exceed (>) its monthly costs, C. It is helpful to make a table for values of x, R and C. xR(x)C(x) 0 0.95 28000 1 (0.95)(2) 28000 + 0.50 2 (0.95)(3) 28000 + 0.50(2) 3 (0.95)(4) 28000 + 0.50(3) From the table R(x) = 0.95x and C(x) = 28000 + 0.50x.

2. Table of Contents Linear Inequalities: Application Slide 2 Since R(x) must be greater than C(x) to obtain a profit, 0.95x > 28000 + 0.50x. From the preceding slide, R(x) = 0.95x and C(x) = 28000 + 0.50x. Last, solve the linear inequality.0.45x > 28000 x > 62,222.2 The company needs to make and sell 62,223 or more compact discs each month to make a profit.

3. Table of Contents Linear Inequalities: Application Try:Sandra plans to make dolls for sell at a local fair booth. She plans on selling each doll for $12.95. It will cost $75 to rent a booth at the fair, and it costs her $8.35 in materials to make each doll. How many dolls will she need to make and sell to make a profit? Write a linear inequality that could be solved to answer this question. Slide 3 12.95x > 75 + 8.35x Solve the linear inequality and answer this question x > 16.30She needs to make and sell 17 or more dolls to make a profit.

4. Table of Contents Linear Inequalities: Application