Questions: Assume the total monthly operating costs of a McDonald's restaurant are: Y= 40,000+ 0.75 X, where X= Number of salad orders and Y= total monthly operating costs. What is the monthly volume at which the average cost per serving is 3.25?

Assume the total monthly operating costs of a McDonald's restaurant are: Y= 40,000+ 0.75 X, where X= Number of salad orders and Y= total monthly operating costs. What is the monthly volume at which the average cost per serving is 3.25?

Transcript text: Assume the total monthly operating costs of a McDonald's restaurant are: $Y=$ $\$ 40,000+\$ 0.75 X$, where $X=$ Number of salad orders and $Y=$ total monthly operating costs. What is the monthly volume at which the average cost per serving is $\$ 3.25$?

Solution

Solution Steps

To find the monthly volume at which the average cost per serving is $3.25, we need to set up an equation where the total cost $Y$ divided by the number of salad orders $X$ equals $3.25. We will solve for $X$ using the given cost equation $Y = 40,000 + 0.75X$.

Step 1: Set Up the Equation

We start with the total monthly operating costs given by the equation: \[ Y = 40000 + 0.75X \] where $Y$ is the total monthly operating costs and $X$ is the number of salad orders.

Step 2: Average Cost Equation

The average cost per serving is defined as: \[ \text{Average Cost} = \frac{Y}{X} \] Setting this equal to the given average cost of $3.25$: \[ \frac{40000 + 0.75X}{X} = 3.25 \]

Step 3: Solve for $X$

To find $X$, we rearrange the equation: \[ 40000 + 0.75X = 3.25X \] This simplifies to: \[ 40000 = 3.25X - 0.75X \] \[ 40000 = 2.5X \] Now, solving for $X$: \[ X = \frac{40000}{2.5} = 16000 \]