A company is planning to make a new kind of radio. The cost to produce \(x\) radios is \(C(x) = 80,000 + 10x\). Meanwhile, the revenue earned by selling \(x\) radios is given by \(R(x) = 18x\). If \(R < C\), the company loses money. At what level of production does this happen?

C ( x ) = 80 , 000 + 10 x ∧ R ( x ) = 18 x R < C ⇔ 18 x < 80 , 000 + 10 x 8 x < 80 , 000 / : 8 x < 10 , 000 A n s . T h e co m p an y l oses m o n ey a t l e v e l o f p ro d u c t i o n 10 , 000 r a d i os .

Answered by kate200468 | 2024-06-10

A company's profitability can be determined by comparing its revenue function, R(x) = 18x, with its cost function, C(x) = 80,000 + 10x. The company suffers losses wherever the cost function exceeds the revenue function. To find the production level where losses occur, we need to solve for x in the inequality R(x) < C(x).
Step-by-Step Calculation:
Set up the inequality: 18x < 80,000 + 10x.
Subtract 10x from both sides of the inequality: 8x < 80,000.
Divide both sides by 8 to solve for x: x < 10,000.
Thus, the company will incur losses when producing fewer than 10,000 radios.

Answered by BenicioBrody | 2024-06-24

The company begins to lose money when it produces fewer than 10,000 radios. At this production level, the revenue is less than the cost. Thus, the company needs to produce at least 10,000 radios to break even and start generating profit.
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Answered by kate200468 | 2024-09-01