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The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells external hard drives. The solid line represents the revenue​ function, Upper R left parenthesis x right parenthesis equals 40 x​; the dashed line represents the cost​ function, Upper C left parenthesis x right parenthesis equals 10 comma 000 plus 20 x.

Use the formulas to find ​R(350​)minus​C(350​). Describe what this means for the company.
Hard Drives Produced and Sold
0
200
400
600
800
0
10,000
20,000
30,000
40,000
x
y
Upper R left parenthesis x right parenthesis equals 40 xUpper C left parenthesis x right parenthesis equals 10 comma 000 plus 20 x

A coordinate plane has a horizontal x-axis labeled Hard Drives Produced and Sold from 0 to 800 in increments of 100 and a vertical y-axis labeled from 0 to 40000 in increments of 5000. A solid line labeled R (x) = 40 x rises from left to right from the origin and through the point (450, 18000). A dashed line labeled C (x) = 10,000 + 20 x rises from left to right from (0, 10000) and through the point (550, 21000). All coordinates are approximate.
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Part 1
​R(350​)minus​C(350​)equals
  
enter your response here
​(Type an integer or a​ decimal.)

1 answer

To compute \( R(350) - C(350) \), we first need to find \( R(350) \) and \( C(350) \) using the given functions for revenue and cost.

  1. Revenue Function:
    The revenue function is given by \[ R(x) = 40x. \] Substituting \( x = 350 \): \[ R(350) = 40 \cdot 350 = 14000. \]

  2. Cost Function:
    The cost function is given by \[ C(x) = 10,000 + 20x. \] Substituting \( x = 350 \): \[ C(350) = 10,000 + 20 \cdot 350 = 10,000 + 7000 = 17000. \]

  3. Calculating \( R(350) - C(350) \): Now we can find \[ R(350) - C(350) = 14000 - 17000 = -3000. \]

Thus, the result is \[ R(350) - C(350) = -3000. \]

Interpretation:

This negative result indicates that when the company produces and sells 350 external hard drives, it incurs a loss of $3000. This implies that the revenue generated from selling those hard drives is not sufficient to cover the total costs associated with producing them. The company needs to either increase sales, lower costs, or both, to achieve profitability.