High School

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Joyce Murphy runs a counter service in downtown Seattle. She charges clients $0.59 per mile driven. Joyce has determined that if she drives 3,500 miles in a month, her total operating cost is $830. If she drives 4,800 miles in a month, her total operating cost is $973. Joyce has used the high-low method to determine that her monthly cost equation is:

Total monthly cost = $445 + $0.11 per mile driven.

Required:
1. Determine how many miles Joyce needs to drive to break even.
2. Calculate Joyce's degree of operating leverage if she drives 5,000 miles.
3. Suppose Joyce took a week off and her sales for the month decreased by 27 percent. Using the degree of operating leverage, calculate the effect this will have on her profit for that month.

Answer :

Joyce needs to drive 3,500 miles to break even. The effect on her profit for that month will be DOL * -27%.

1. To determine how many miles Joyce needs to drive to break even, we can set up an equation using the given information. Let's assume x represents the number of miles Joyce needs to drive to break even. According to the high-low method, the monthly cost equation is total monthly cost = 445 + 0.11 per mile driven.

Setting up the equation:
830 = 445 + 0.11(3,500)
973 = 445 + 0.11(4,800)

Solving the equations:
830 = 445 + 385
973 = 445 + 528

By subtracting $from both sides of the equations, we can find the cost per mile:
385 = 0.11(3,500)
528 = 0.11(4,800)

Dividing both sides of the equations by 0.11, we can find the number of miles:
3,500 = x
4,800 = x


2. To calculate Joyce's degree of operating leverage if she drives 5,000 miles, we can use the formula: Degree of Operating Leverage (DOL) = % Change in Profit / % Change in Sales.

Given that Joyce's sales for the month decreased by 27%, we can calculate the effect on profit. Let's assume the original profit is P1 and the new profit is P2.

% Change in Sales = -27%
% Change in Profit = (P2 - P1) / P1

Using the formula, we can calculate the degree of operating leverage:
DOL = % Change in Profit / % Change in Sales
DOL = ((P2 - P1) / P1) / (-27/100)

Let's say P1 = profit with sales before the decrease, and P2 = profit with decreased sales.

3. Suppose Joyce took a week off and her sales for the month decreased by 27 percent. Using the degree of operating leverage, we can calculate the effect this will have on her profit for that month. By substituting the values into the formula, we can calculate the % Change in Profit.

%D Change in Profit = DOL * %D Change in Sales

Let's assume the %D Change in Sales is -27% and Joyce's degree of operating leverage is calculated to be DOL.

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