The following are exercises for module 1 (Ch 1) of the learning objectives in Math 1324. 1.) A manufacturer's cost to manufacture 50 microwaves is $14,040, while the cost to make 400 microwaves is $28,040. Let x = number of microwaves and y = cost . a.) Assuming the cost function is linear find the cost function using algebraic methods. Show work. b.) From the cost function, state and interpret the average rate of change in the cost to make a microwave. c.) What are this manufacturer's fixed costs? d.) This manufacturer will sell these microwaves for $79.00 each. State the linear revenue function. e.) Using algebraic methods, find the breakeven point for the microwave manufacturer. f.) Using a complete sentence, explain what this breakeven point means in this problem. 2.) A drugstore sells a drug costing $85 for $112 and a drug costing $175 for $238. What the drugstore pays for the drug is called the wholesale price (C) and the amount they sell it for is called the retail price (R). The amount by which the drugstore increases the cost of the drug is called the markup. a) If the markup policy of the drugstore is assumed to be linear, use algebraic methods to find an equation that expresses retail price R in terms of cost C. b.) What does a store pay (to the nearest dollar) for a drug that retails for $185 ? 3.) The supply and demand equations for a product are given as: supply: p = 4q + 5 demand 2q + p = 77 a.) How many units are demanded when the price is $ 50 ? ___________________ b.) How many units are supplied when the price is $50 ? ___________________ c.) When the price is $50 is there a shortage of the product or a surplus? ________________ d.) Find the equilibrium quantity and price. Use algebraic methods. e.) Using a complete sentence, explain what the answer in part (d) means with regard to this problem. 4.) Let the supply and demand for bananas in cents per pound be given by : supply: p = 52 q demand: p =100 - 52 q a.) Graph these equations on the same axes. b.) Find the equilibrium quantity and price. Use algebraic methods. c.) On what interval of the graph ( referring to "q") does demand exceed supply? Math 1324 Module 1 Page 1 5.) A company produces a certain toy and finds that the cost of producing x toys is given by the function C(x) = 1.50x + 7500. The revenue from selling x toys is given by the function R(x) = 6.50x. a.) What is the marginal cost? ______________ b.) What are the fixed costs for this company? ___________________ c.) What is the marginal revenue? _______________ d.) What will it cost the company to make 5000 of the toys? __________________ e.) What revenue will result from the sale of 375 of the toys?______________ f.) Find the break-even point algebraically. Show work. g.) Find the profit function for the sale of this toy. P(x) = _________________________________ h.) What is the marginal profit? _______________ 6.) On the basis of data from 1990 to 2006, the median income (y) in year x for men and women is approximated by the equations: Men: Women -247x + 2y = 61,552 -854x + 3y = 45,765 where x=0 corresponds to 1990. If these equations remain valid in the future, in what year will the median income for men and women be the same? Math 1324 Module 1 Page 2