## Thinking Mathematically (6th Edition)

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.