a business that manufactures small alarm clocks has weekly fixed costs of $6000. the average cost per clock…

a business that manufactures small alarm clocks has weekly fixed costs of $6000. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.4x + 6000}{x}$. a. find the average cost when x = 100, 1000, and 10,000. b. like all other businesses, the alarm clock manufacturer must make a profit. to do this, each clock must be sold for at least 50¢ more than what it costs to manufacture. due to competition from a larger company, the clocks can be sold for $1.50 each and no more. our small manufacturer can only produce 2000 clocks weekly. does this business have much of a future? explain. a. the average cost when x = 100 is $ . (type an integer or a decimal.) the average cost when x = 1000 is $ . (type an integer or a decimal.) the average cost when x = 10,000 is $ . (type an integer or a decimal.) b. does this business have much of a future?

a business that manufactures small alarm clocks has weekly fixed costs of $6000. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.4x + 6000}{x}$. a. find the average cost when x = 100, 1000, and 10,000. b. like all other businesses, the alarm clock manufacturer must make a profit. to do this, each clock must be sold for at least 50¢ more than what it costs to manufacture. due to competition from a larger company, the clocks can be sold for $1.50 each and no more. our small manufacturer can only produce 2000 clocks weekly. does this business have much of a future? explain. a. the average cost when x = 100 is $ . (type an integer or a decimal.) the average cost when x = 1000 is $ . (type an integer or a decimal.) the average cost when x = 10,000 is $ . (type an integer or a decimal.) b. does this business have much of a future?

Answer

Explanation:

Step1: Substitute x = 100

Substitute x = 100 into $\frac{0.4x + 6000}{x}$: $\frac{0.4\times100+6000}{100}=\frac{40 + 6000}{100}=\frac{6040}{100}=60.4$

Step2: Substitute x = 1000

Substitute x = 1000 into $\frac{0.4x + 6000}{x}$: $\frac{0.4\times1000+6000}{1000}=\frac{400+6000}{1000}=\frac{6400}{1000}=6.4$

Step3: Substitute x = 10000

Substitute x = 10000 into $\frac{0.4x + 6000}{x}$: $\frac{0.4\times10000+6000}{10000}=\frac{4000+6000}{10000}=\frac{10000}{10000}=1$

Step4: Analyze profitability

The cost per - clock when x = 2000 is $\frac{0.4\times2000+6000}{2000}=\frac{800 + 6000}{2000}=\frac{6800}{2000}=3.4$. The selling price is $1.50 per clock. Since the cost per clock ($3.4$) is greater than the selling price ($1.50$), the business is not profitable.

Answer:

a. The average cost when x = 100 is $60.4$. The average cost when x = 1000 is $6.4$. The average cost when x = 10000 is $1$. b. No, the business does not have much of a future because the cost per clock ($3.4$ when producing 2000 clocks) is greater than the selling price per clock ($1.50$), resulting in a loss.