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.

Question

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.
Question content area bottom
Part 1
​R(350​)minus​C(350​)equals
  
negative 3000.
​(Type an integer or a​ decimal.)
Part 2
Describe what this means for the company.
When the company produces and sells 
  
enter your response here hard​ drives, the 
▼ 
loss
gain
 for the company is ​$
  
enter your response here.

GPT-4o mini · Answer

To find $ R(350) - C(350) $, we need to calculate the revenue and cost at $ x = 350 $. 1. **Calculate Revenue**: $$ R(x) = 40x $$ $$ R(350) = 40 \times 350 = 14000 $$ 2. **Calculate Cost**: $$ C(x) = 10000 + 20x $$ $$ C(350) = 10000 + 20 \times 350 = 10000 + 7000 = 17000 $$ 3. **Calculate $ R(350) - C(350) $**: $$ R(350) - C(350) = 14000 - 17000 = -3000 $$ ### Part 1 Answer: $$ R(350) - C(350) = -3000 $$ ### Part 2 Answer: This means that when the company produces and sells **350 hard drives**, the **loss** for the company is **$3000**. In summary, the company is operating at a loss of $3000 when producing and selling 350 hard drives, indicating that their costs exceed their revenues at this production level.