a business that manufactures small alarm clocks has weekly fixed costs of $6500. the average cost per clock…

a business that manufactures small alarm clocks has weekly fixed costs of $6500. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.7x + 6500}{x}$. 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. (type an integer or a decimal.) the average cost when x = 1000 is $ 7.2 (type an integer or a decimal.) the average cost when x = 10,000 is $ 1.35 (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 $6500. the average cost per clock for the business to manufacture x clocks is described by $\frac{0.7x + 6500}{x}$. 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. (type an integer or a decimal.) the average cost when x = 1000 is $ 7.2 (type an integer or a decimal.) the average cost when x = 10,000 is $ 1.35 (type an integer or a decimal.) b. does this business have much of a future?

Answer

Explanation:

Step1: Calculate average cost for x = 100

Substitute x = 100 into $\frac{0.7x + 6500}{x}$: $\frac{0.7\times100+6500}{100}=\frac{70 + 6500}{100}=\frac{6570}{100}=65.7$

Step2: Given values for x = 1000 and x = 10000

We already know from the problem - statement that when x = 1000, the average cost is $7.2$ and when x = 10000, the average cost is $1.35$

Step3: Analyze profitability for part b

The selling - price per clock is $1.50$. The manufacturer needs to sell each clock for at least 50 cents more than the cost price to make a profit. The maximum production is x = 2000. Substitute x = 2000 into the average - cost formula $\frac{0.7x + 6500}{x}$: $\frac{0.7\times2000+6500}{2000}=\frac{1400 + 6500}{2000}=\frac{7900}{2000}=3.95$. Since $3.95>1.50$, the cost per clock is higher than the selling price per clock when producing the maximum number of 2000 clocks.

Answer:

a. When x = 100, the average cost is $65.7$. When x = 1000, the average cost is $7.2$. When x = 10000, the average cost is $1.35$. b. No, this business does not have much of a future. When the manufacturer produces the maximum of 2000 clocks per week, the average cost per clock ($3.95$) is higher than the selling price per clock ($1.50$), so it will not make a profit.