a business that manufactures small alarm clocks has weekly fixed costs of $4500. the average cost per clock…

a business that manufactures small alarm clocks has weekly fixed costs of $4500. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.6x + 4500}{x}$. 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.)

a business that manufactures small alarm clocks has weekly fixed costs of $4500. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.6x + 4500}{x}$. 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.)

Answer

Explanation:

Step1: Substitute x = 100

Substitute x = 100 into $\frac{0.6x + 4500}{x}$: $\frac{0.6\times100+4500}{100}=\frac{60 + 4500}{100}=\frac{4560}{100}=45.6$

Step2: Substitute x = 1000

Substitute x = 1000 into $\frac{0.6x + 4500}{x}$: $\frac{0.6\times1000+4500}{1000}=\frac{600+4500}{1000}=\frac{5100}{1000}=5.1$

Step3: Substitute x = 10000

Substitute x = 10000 into $\frac{0.6x + 4500}{x}$: $\frac{0.6\times10000+4500}{10000}=\frac{6000 + 4500}{10000}=\frac{10500}{10000}=1.05$

Step4: Analyze profit - making ability

The selling price is $1.50 per clock. The maximum number of clocks produced per week is x = 2000. The average cost per clock when x = 2000 is $\frac{0.6\times2000+4500}{2000}=\frac{1200 + 4500}{2000}=\frac{5700}{2000}=2.85$. Since $2.85>1.50$, the cost per clock is higher than the selling - price, so the business has little future.

Answer:

The average cost when x = 100 is $45.6$ The average cost when x = 1000 is $5.1$ The average cost when x = 10000 is $1.05$ The business has little future because when the maximum production of 2000 clocks per week is considered, the average cost per clock ($2.85$) is higher than the selling price ($1.50$) per clock.