Variable Cost and Total Revenue Function
BUSINESS MATHEMATICS: ASSIGNMENT - “Section” 5.1, page 182.
(1) Write the general form of a linear function involving five independent variables. (2) Assume that the salesperson in Example 1 (page 177) has a salary goal of $800 per week. If product B is not available one week, how many units of product A must be sold to meet the salary goal? If product A is unavailable, how many units be sold of product B? (3) Assume in Example 1 (page 177) that the salesperson receives a bonus when combined sales from the two products exceed 80 units. The bonus is $2.50 per unit for each unit over 80. With this incentive program, the salary function must be described by two different linear functions. What are they, and when are they valid.
(4) For Example 4 (page 181), how many units be produced and sold in order to (a) earn a profit of $1.5 million, and (b) earn zero profit (break even)?
(5) A manufacturer of microcomputers produces three different models. The following table summarizes wholesale prices, material cost per unit, and labor cost per unit. Annual fixed costs are $25 million.
________________________________________ __________Microcomputers_________ Model 1 Model 2 __ Model 3 Wholesale price/unit $500 $1,000 $1,500 Material cost/unit 175 400 750 Labor cost/unit 100 150 225 ________________________________________ (a) Determine a joint total revenue function of the three different microcomputer models. (b) Determine an annual cost function for manufacturing the three models. (c) Determine the profit function for sales of the three models.
(1) Write the general form of a linear function involving five independent variables. (2) Assume that the salesperson in Example 1 (page 177) has a salary goal of $800 per week. If product B is not available one week, how many units of product A must be sold to meet the salary goal? If product A is unavailable, how many units be sold of product B? (3) Assume in Example 1 (page 177) that the salesperson receives a bonus when combined sales from the two products exceed 80 units. The bonus is $2.50 per unit for each unit over 80. With this incentive program, the salary function must be described by two different linear functions. What are they, and when are they valid.
(4) For Example 4 (page 181), how many units be produced and sold in order to (a) earn a profit of $1.5 million, and (b) earn zero profit (break even)?
(5) A manufacturer of microcomputers produces three different models. The following table summarizes wholesale prices, material cost per unit, and labor cost per unit. Annual fixed costs are $25 million.
________________________________________ __________Microcomputers_________ Model 1 Model 2 __ Model 3 Wholesale price/unit $500 $1,000 $1,500 Material cost/unit 175 400 750 Labor cost/unit 100 150 225 ________________________________________ (a) Determine a joint total revenue function of the three different microcomputer models. (b) Determine an annual cost function for manufacturing the three models. (c) Determine the profit function for sales of the three models.