The graph shows the cost and revenue equations for a product. The x y-coordinate plane is given. The horizontal axis is labeled Number of units and the vertical axis is labeled Dollars . There are 2 lines on the graph. The line labeled C = 0.5x + 4,000 enters the window at y = 4,000 on the positive y-axis, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled R = 0.9x, and exits the window in the first quadrant. The line labeled R = 0.9x enters the window at the origin, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled C = 0.5x + 4,000, and exits the window in the first quadrant. (a) For what number of units sold does the company break even?   units (b) For what numbers of units sold is there a loss for the company? If less than   units are sold, the company loses money. (c) For what numbers of units sold is there a profit for the company? If more than   units are sold, the company makes a profit.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
The graph shows the cost and revenue equations for a product.
The x y-coordinate plane is given. The horizontal axis is labeled Number of units and the vertical axis is labeled Dollars . There are 2 lines on the graph.
  • The line labeled C = 0.5x + 4,000 enters the window at y = 4,000 on the positive y-axis, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled R = 0.9x, and exits the window in the first quadrant.
  • The line labeled R = 0.9x enters the window at the origin, goes up and right, passes through the point (10,000, 9,000) crossing the line labeled C = 0.5x + 4,000, and exits the window in the first quadrant.
(a)
For what number of units sold does the company break even?
  units
(b)
For what numbers of units sold is there a loss for the company?
If less than   units are sold, the company loses money.
(c)
For what numbers of units sold is there a profit for the company?
If more than   units are sold, the company makes a profit.
 
Expert Solution
Step 1: Given.

Given: The cost and revenue functions are given by C(x)=0.5x+4000 and R(x)=0.9x.

To find: (a) For what number of units sold does the company break-even?

(b) For what number of units sold is there a loss for the company?

(c) For what numbers of units sold is there a profit for the company?

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