Based on surveys conducted in your area, you determine that it is feasible to sell your specialty pizzas for $15. The cost for making the pizzas includes a fixed cost of $55 and a labor cost of $4 per pizza.

Establish an equation to determine revenue. Establish an equation to determine total cost.
How many pizzas must be sold to break even (i.e., you experience neither a profit nor a loss)? Interpret your result.
As a business owner, it is very important to have an understanding of profit and loss. The formula for determining profit is Profit = revenue – cost (P = R – C).
Determine the profit if 500 specialty pizzas are sold. Interpret your result.
How many specialty pizzas would need to be sold to make a profit of $1,100? Interpret your result.

To establish the equation to determine revenue, we need to multiply the selling price ($15) by the number of pizzas sold (x):

Revenue = Selling price * Number of pizzas sold
R = 15x

To establish the equation to determine the total cost, we need to add the fixed cost ($55) and the labor cost per pizza ($4) multiplied by the number of pizzas sold (x):

Total Cost = Fixed cost + Labor cost per pizza * Number of pizzas sold
C = 55 + 4x

To determine the number of pizzas that must be sold to break even, we can set the profit (P) to 0 in the profit formula:

P = R - C
0 = 15x - (55 + 4x)

Simplifying the equation:
0 = 15x - 55 - 4x
0 = 11x - 55

Solving for x:
11x = 55
x = 55/11
x = 5

Interpretation: To break even, you would need to sell 5 specialty pizzas. This means that your revenue would exactly cover your total cost, resulting in neither a profit nor a loss.

To determine the profit if 500 specialty pizzas are sold, we can use the profit formula:

P = R - C
P = 15(500) - (55 + 4(500))
P = 7500 - (55 + 2000)
P = 7500 - 2055
P = 5445

Interpretation: If 500 specialty pizzas are sold, the profit would be $5,445. This represents the amount you would earn after subtracting the total cost from the revenue.

To determine the number of specialty pizzas that need to be sold to make a profit of $1,100, we can set the profit (P) to $1,100 in the profit formula:

P = R - C
1100 = 15x - (55 + 4x)

Simplifying the equation:
1100 = 15x - 55 - 4x
1100 = 11x - 55

Solving for x:
11x = 1155
x = 1155/11
x ≈ 105

Interpretation: To make a profit of $1,100, approximately 105 specialty pizzas need to be sold. This means that the revenue from selling these pizzas would exceed the total cost by $1,100.