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 10000. 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 = 10000 is $1 (type an integer or a decimal.) b. does this business have much of a future? a. no, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks b. yes, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks c. yes, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks d. no, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks

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 10000. 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 = 10000 is $1 (type an integer or a decimal.) b. does this business have much of a future? a. no, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks b. yes, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks c. yes, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks d. no, the average cost to produce 2000 alarm clocks is much less than the selling price of the alarm clocks

Answer

Explanation:

Step1: Calculate average cost for x = 10000

The formula for average cost per clock is $\frac{0.4x + 6000}{x}$. Substitute $x = 10000$ into the formula: $\frac{0.4\times10000+6000}{10000}$. First, calculate the numerator: $0.4\times10000 = 4000$, then $4000 + 6000=10000$. So, $\frac{10000}{10000}=1$.

Step2: Analyze business future

The formula for average cost per clock is $\overline{C}=\frac{0.4x + 6000}{x}=0.4+\frac{6000}{x}$. When $x = 2000$, $\overline{C}=0.4+\frac{6000}{2000}=0.4 + 3=3.4$. The selling - price per clock is $1.5$. Since the average cost of producing 2000 clocks ($3.4$) is much greater than the selling price ($1.5$), the business has no future.

Answer:

a. 1 b. A. No, the average cost to produce 2000 alarm clocks is much greater than the selling price of the alarm clocks