Answer
a. When x = 100, the average cost per clock is 50 dollars and 50 cents.
When x = 1000, the average cost per clock is 5 dollars and 50 cents.
When x = 10,000, the average cost per clock is 1 dollar.
b. This business doesn't have a future if it can only produce 2000 clocks per weekly.
Work Step by Step
Part A
The average cost per clock is $\frac{0.5x + 5000}{x}$
If x = 100 clocks produced, then the average cost per clock is $\frac{(0.5)(100) + 5000}{100}$ = $\frac{50 + 5000}{100}$ = $\frac{5050}{100}$ = 50.50 (50 dollars and 50 cents).
If x = 1000 clocks, the average cost per clock is $\frac{(0.5)(1000) + 5000}{1000}$. This gives us $\frac{500 + 5000}{1000}$ = $\frac{5500}{1000}$ = 5.50 (5 dollars and 50 cents).
If x = 10000 clocks, the average cost per clock is $\frac{(0.5)(10000) + 5000}{10000}$.
This gives us $\frac{5000 + 5000}{10000}$ = $\frac{10000}{10000}$ = 1.00 (1 dollar).
Part B
If the company can produce 2000 clocks per week, the average cost per clock is $\frac{(0.5)(2000) + 5000}{2000}$ = $\frac{1000 + 5000}{2000}$ = $\frac{6000}{2000}$ = 3.00 (3 dollars).
If the company must sell them for 50 cents more than the cost of making them (in order to make a profit(, this means they must sell each clock of 3.50 (3 dollars and 50 cents).
They have a competitor that sells the clock of 1.50 (1 dollar 50 cents). This is 2 dollars below the company we are looking at, so only making 2000 clocks per week will not be profitable. Therefore the business doesn't have a future.
