Answer:
To make a profit in the first year of business, the company needs to sell enough small and large cheese pizzas with their respective boxes to generate more revenue than the cost of making and packaging the pizzas.
Similarly, to make a profit in the second year, the company needs to sell enough small and large cheese pizzas with their respective boxes to generate more revenue than the cost of making and packaging the pizzas. Different combinations of pizzas and boxes can be used to achieve a profit, as long as the total revenue generated is greater than the total cost incurred.
Explanation:
To find the profit for each combination of boxes and pizzas, we need to subtract the total cost from the total revenue. Let's call the number of small cheese pizzas sold S, the number of large cheese pizzas sold L, the number of small boxes used for the small pizzas B1, and the number of large boxes used for the large pizzas B2. Then, the profit for each year can be calculated as follows:
First year profit:
Total revenue = 9S + 14.25L
Total cost = 2.5S + 0.25B1 + 4.15L + 0.5B2
Profit = Total revenue - Total cost
Profit = 9S + 14.25L - 2.5S - 0.25B1 - 4.15L - 0.5B2
Profit = 6.5S + 10.1L - 0.25B1 - 0.5B2
Second year profit:
Total revenue = 9S + 14.25L
Total cost = 2.5S + 0.25B1 + 4.15L + 0.5B2
Profit = Total revenue - Total cost
Profit = 9S + 14.25L - 2.5S - 0.25B1 - 4.15L - 0.5B2
Profit = 6.5S + 10.1L - 0.25B1 - 0.5B2
To have a profit for the first year, the profit equation should be greater than 0. We can find different combinations of S, L, B1, and B2 that will satisfy this condition. Here are a few examples:
Sell 10 small cheese pizzas and 5 large cheese pizzas. Use 20 small boxes and 10 large boxes.
Profit = 6.5(10) + 10.1(5) - 0.25(20) - 0.5(10) = $55.75
Sell 20 small cheese pizzas and 10 large cheese pizzas. Use 40 small boxes and 20 large boxes.
Profit = 6.5(20) + 10.1(10) - 0.25(40) - 0.5(20) = $111.50
Sell 30 small cheese pizzas and 15 large cheese pizzas. Use 60 small boxes and 30 large boxes.
Profit = 6.5(30) + 10.1(15) - 0.25(60) - 0.5(30) = $167.25
Similarly, to have a profit for the second year, the profit equation should be greater than 0. We can find different combinations of S, L, B1, and B2 that will satisfy this condition. Here are a few examples:
Sell 15 small cheese pizzas and 7 large cheese pizzas. Use 30 small boxes and 15 large boxes.
Profit = 6.5(15) + 10.1(7) - 0.25(30) - 0.5(15) = $89.65
Sell 25 small cheese pizzas and 12 large cheese pizzas. Use 50 small boxes and 24 large boxes.
Profit = 6.5(25) + 10.1(12) - 0.25(50) - 0.5(24) = $166.65
Sell 35 small cheese pizzas and 17 large cheese pizzas. Use 70 small boxes and 34 large boxes.
Profit