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 $\frac{0.7x + 6000}{x}$. 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 $\frac{0.7x + 6000}{x}$. 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 into formula

$\frac{0.7\times100 + 6000}{100}=\frac{70+6000}{100}=\frac{6070}{100}=60.7$

Step2: Substitute x = 1000 into formula

$\frac{0.7\times1000 + 6000}{1000}=\frac{700 + 6000}{1000}=\frac{6700}{1000}=6.7$

Step3: Substitute x = 10000 into formula

$\frac{0.7\times10000+6000}{10000}=\frac{7000 + 6000}{10000}=\frac{13000}{10000}=1.3$

Step4: Analyze profit - making ability

When x = 2000, the average cost per clock is $\frac{0.7\times2000+6000}{2000}=\frac{1400 + 6000}{2000}=\frac{7400}{2000}=3.7$. The selling - price is $1.50$ per clock. Since the selling price ($1.50$) is less than the average cost ($3.7$) when producing the maximum number of 2000 clocks per week, the business is operating at a loss and does not have much of a future.

Answer:

a. The average cost when x = 100 is $60.7$ The average cost when x = 1000 is $6.7$ The average cost when x = 10000 is $1.3$ b. No. Because when producing the maximum number of 2000 clocks per week, the average cost per clock ($3.7$) is higher than the selling price per clock ($1.50$), so the business is operating at a loss.