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1. Suppose that when a company produces its product, fixed costs are $12,500 and variable cost per item is $75. (a) Write the total cost function if x represents the number of units. (b) Are fixed costs equal to C(0)? 2. Suppose the company in Problem 1 sells its product for $175 per item. (a) Write the total revenue function. (b) Find R(100) and give its meaning. 3. (a) Give the formula for profit in terms of revenue and cost. (b) Find the profit function for the company in Problems 1 and 2.

1. Suppose that when a company produces its product, fixed costs are $12,500 and variable cost per item is $75. (a) Write the total cost function if x represents the number of units. (b) Are fixed costs equal to C(0)? 2. Suppose the company in Problem 1 sells its product for $175 per item. (a) Write the total revenue function. (b) Find R(100) and give its meaning. 3. (a) Give the formula for profit in terms of revenue and cost. (b) Find the profit function for the company in Problems 1 and 2.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Please answer Checkpoints 1-4?
106 CHAPTER 1 Linear Equations and Functions MOIT3 2800 Break-even R(x)= 10x 1200 point (160, 1600) 2400 Profit region P(x)=7.50x–1200 800 2000+ Break-even Profit 1600 + C 400 + region श्रीती point 1200- Loss C(x) = 2.50x+1200 120 160 280 40 200 800 + region -400 +Loss -region 400 + -800 40 120 200 280 -1200 T Figure 1.32 le om Figure 1.33 The profit function for Example 3 is given by P(x) R(x) – C(x) = 10x - (2.50x + 1200) or P(x) = 7.50x – 1200 We can find the point where the profit is zero (the break-even point) by setting P(x) = 0 and solving for x. 0 = 7.50x – 1200= 1200 = 7.50x= x = 160 b Note that this is the same break-even quantity that we found by solving the total reve- nue and total cost equations simultaneously (see Figure 1.33). CHECKPOINT 4. Identify two ways in which break-even can be found.
Transcribed Image Text:106 CHAPTER 1 Linear Equations and Functions MOIT3 2800 Break-even R(x)= 10x 1200 point (160, 1600) 2400 Profit region P(x)=7.50x–1200 800 2000+ Break-even Profit 1600 + C 400 + region श्रीती point 1200- Loss C(x) = 2.50x+1200 120 160 280 40 200 800 + region -400 +Loss -region 400 + -800 40 120 200 280 -1200 T Figure 1.32 le om Figure 1.33 The profit function for Example 3 is given by P(x) R(x) – C(x) = 10x - (2.50x + 1200) or P(x) = 7.50x – 1200 We can find the point where the profit is zero (the break-even point) by setting P(x) = 0 and solving for x. 0 = 7.50x – 1200= 1200 = 7.50x= x = 160 b Note that this is the same break-even quantity that we found by solving the total reve- nue and total cost equations simultaneously (see Figure 1.33). CHECKPOINT 4. Identify two ways in which break-even can be found.
EXAMPLE Marginal Cost Suppose that the cost (in dollars) for a product is C = 21.75x + 4890. What is the mar- ginal cost for this product, and what does it mean? Solution The equation has the form C = mx + b, so the slope is 21.75. Thus the marginal cost is MC = 21.75 dollars per unit. Because the marginal cost is the slope of the cost line, production of each additional unit will cost $21.75 more, at any level of production. Note that when total cost functions are linear, the marginal cost is the same as the variable cost per unit. This is not the case if the functions are not linear, as we shall see later. CHECKРOINT 1. Suppose that when a company produces its product, fixed costs are $12,500 and variable cost per item is $75. (a) Write the total cost function if x represents the number of units. (b) Are fixed costs equal to C(0)? 2. Suppose the company in Problem 1 sells its product for $175 (a) Write the total revenue function. (b) Find R(100) and give its meaning. 3. (a) Give the formula for profit in terms of revenue and cost. (b) Find the profit function for the company in Problems 1 and 2. per item. Break-Even Analysis We can solve the equations for total revenue and total cost simultaneously to find the point where cost and revenue are equal. This point is called the break-even point. Graphically the break-even point is the point of intersection of the graphs of the total revenue function and the total cost function.
Transcribed Image Text:EXAMPLE Marginal Cost Suppose that the cost (in dollars) for a product is C = 21.75x + 4890. What is the mar- ginal cost for this product, and what does it mean? Solution The equation has the form C = mx + b, so the slope is 21.75. Thus the marginal cost is MC = 21.75 dollars per unit. Because the marginal cost is the slope of the cost line, production of each additional unit will cost $21.75 more, at any level of production. Note that when total cost functions are linear, the marginal cost is the same as the variable cost per unit. This is not the case if the functions are not linear, as we shall see later. CHECKРOINT 1. Suppose that when a company produces its product, fixed costs are $12,500 and variable cost per item is $75. (a) Write the total cost function if x represents the number of units. (b) Are fixed costs equal to C(0)? 2. Suppose the company in Problem 1 sells its product for $175 (a) Write the total revenue function. (b) Find R(100) and give its meaning. 3. (a) Give the formula for profit in terms of revenue and cost. (b) Find the profit function for the company in Problems 1 and 2. per item. Break-Even Analysis We can solve the equations for total revenue and total cost simultaneously to find the point where cost and revenue are equal. This point is called the break-even point. Graphically the break-even point is the point of intersection of the graphs of the total revenue function and the total cost function.
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