A popular donut shop spends \( \$ 0.10 \) per donut to produce their award-winning donuts. I addition, they pay \( \$ 1100 \) in utilities and \( \$ 5100 \) in salaries and benefits per month. a) Defining \( E \) as the total monthly expenses and \( d \) as the number of donuts produced, write an equation of the expenses to the number of donuts. Equation: b) The store manager calculated the total expenses for March as \( \$ 14150 \). Use the equati to determine how many donuts were produced in March. Round to the nearest whole donut. c) The shop sells each donut for \( \$ 0.50 \). What was the shop's revenue in March? Revenue in March: \( \$ \square \) d) How much profit did the store make in March? Profit: \( \$ \)

To solve the problem, let's break it down step by step. ### a) Write an equation for total monthly expenses \( E \) in terms of the number of donuts \( d \). The total monthly expenses \( E \) can be calculated as the sum of the variable costs (cost per donut multiplied by the number of donuts) and the fixed costs (utilities and salaries). - Cost per donut: \( \$0.10 \) - Fixed costs (utilities + salaries): \( \$1100 + \$5100 = \$6200 \) The equation for total expenses \( E \) is: \[ E = 0.10d + 6200 \] ### b) Determine how many donuts were produced in March if the total expenses were \( \$14150 \). We can set the total expenses equal to the calculated expenses equation: \[ 14150 = 0.10d + 6200 \] Now, we can solve for \( d \): 1. Subtract \( 6200 \) from both sides: \[ 14150 - 6200 = 0.10d \] \[ 7930 = 0.10d \] 2. Divide both sides by \( 0.10 \): \[ d = \frac{7930}{0.10} = 79300 \] So, the number of donuts produced in March is \( 79300 \). ### c) Calculate the shop's revenue in March. The shop sells each donut for \( \$0.50 \). Therefore, the revenue \( R \) can be calculated as: \[ R = \text{price per donut} \times \text{number of donuts} \] \[ R = 0.50 \times 79300 \] \[ R = 39650 \] So, the revenue in March is \( \$39650 \). ### d) Calculate the profit made by the store in March. Profit can be calculated as the difference between revenue and expenses: \[ \text{Profit} = R - E \] \[ \text{Profit} = 39650 - 14150 \] \[ \text{Profit} = 25500 \] So, the profit made by the store in March is \( \$25500 \). ### Summary of Answers: - a) Equation: \( E = 0.10d + 6200 \) - b) Donuts produced: \( 79300 \) - c) Revenue in March: \( \$39650 \) - d) Profit: \( \$25500 \)