A shop sells coffee and donuts. The coffee sells for $4.31 and donuts for $0.83 apiece. The cost to produce a cup of coffee is $1.50 and the cost to make a donut is $0.76. In month 1 the quantity of coffee sold is 1,283 and donuts sold was 216. In month 2 the quantity of coffee sold is 4,210 and donuts sold was 317.

a) Calculate the profit for month 1 and 2 for both coffee and donuts.

My answer for Month 1 is coffee profit is $3,605.23 and donut profit is $15.12. Month 2 coffee profit is $11,830.10 and donut profit is $23.59. Is this correct?

b) In month 3 the coffee profit is $8,763 and the donut profit is $99.99. What is the quantity of donuts and coffee sold?

My answer is 3,118 cups of coffee sold and 1,428 donuts sold. Is this correct?

a. Month 1:

Profit = (4.31-1.50)/cup * 1283cups =
$3605.23

Profit = (0.83-0.76)/donut * 216Donuts =
$15.12

Month 2:
Profit = (4.31-1.50)/cup * 4210cups =
$11,830.10

Profit = (0.83-0.76)/donut * 317Donuts =
$22.19

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To calculate the profit for each month, you need to determine the revenue and the cost for each item (coffee and donuts) separately.

a) For Month 1:
- Revenue from coffee: Quantity of coffee sold * Price per cup of coffee = 1,283 * $4.31 = $5,522.73
- Cost of producing coffee: Quantity of coffee sold * Cost per cup of coffee = 1,283 * $1.50 = $1,924.50
- Coffee profit: Revenue from coffee - Cost of producing coffee = $5,522.73 - $1,924.50 = $3,598.23

- Revenue from donuts: Quantity of donuts sold * Price per donut = 216 * $0.83 = $179.28
- Cost of making donuts: Quantity of donuts sold * Cost per donut = 216 * $0.76 = $164.16
- Donut profit: Revenue from donuts - Cost of making donuts = $179.28 - $164.16 = $15.12

Therefore, the profit for Month 1 is $3,598.23 for coffee and $15.12 for donuts.

Follow the same process for Month 2:
- Coffee profit: $11,830.10
- Donut profit: $23.59

So, your answer for the profit calculations seems correct for Month 2.

b) To find the quantity of donuts and coffee sold in Month 3 given the profit numbers, you need to reverse the calculations.

For coffee:
Revenue from coffee - Cost of producing coffee = Coffee profit
Quantity of coffee sold * Price per cup of coffee - Quantity of coffee sold * Cost per cup of coffee = $8,763
Quantity of coffee sold * ($4.31 - $1.50) = $8,763
Quantity of coffee sold = $8,763 / ($4.31 - $1.50) = 3,118 (rounded to whole numbers)

For donuts:
Revenue from donuts - Cost of making donuts = Donut profit
Quantity of donuts sold * Price per donut - Quantity of donuts sold * Cost per donut = $99.99
Quantity of donuts sold * ($0.83 - $0.76) = $99.99
Quantity of donuts sold = $99.99 / ($0.83 - $0.76) = 1,428 (rounded to whole numbers)

Hence, your answer of 3,118 cups of coffee sold and 1,428 donuts sold in Month 3 seems correct.