As an entrepreneur, there are going to be many decisions that you need to make, such as the price to charge your customers for your goods and services. You have just graduated from college and recently opened a specialty pizza restaurant. 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.
a. Establish an equation to determine revenue.
b. Establish an equation to determine total cost.
c. 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).
d. Determine the profit if 500 specialty pizzas are sold. Interpret your result.
e. How many specialty pizzas would need to be sold to make a profit of $1,100? Interpret your result.
f. How many specialty pizzas would you need to sell if you wanted to make a profit greater than $1,595? Interpret your result.
(a) R = 15p
(b) C = 55 + 4p
(c) Revenue [5*15]= $75
Variable cost [5*4]= $20
contribution 55
fixed cost -55
Net profit. 0
(d) 15p = 55 + 4p
11p = 55
p = 5 pizzas break-even
Profit = revenue - cost
15(500)-4(500)-55 = $5445
Sell 500 pizzas $5445
(e) profit = 15p -55-4p
1100 = 11p -55
1155 = 11p
p = 105
Sell 105 pizzas $1100
(f) 1595 = 11p -55
1650 = 11p
p = 150
Sell 150 pizzas make $1595
a. To establish an equation to determine revenue, we need to consider the price per pizza and the number of pizzas sold. Let's call the number of pizzas sold "x". The equation to determine revenue is:
Revenue = Price per pizza * Number of pizzas sold
In this case, the price per pizza is $15, so the equation becomes:
Revenue = $15 * x
b. To establish an equation to determine total cost, we need to consider the fixed cost and the labor cost per pizza. The fixed cost is $55, and the labor cost per pizza is $4. Let's call the total cost "C" and the number of pizzas sold "x". The equation to determine total cost is:
Total Cost = Fixed Cost + Labor Cost per pizza * Number of pizzas sold
In this case, the equation becomes:
Total Cost = $55 + $4 * x
c. To determine the number of pizzas that must be sold to break even, we need to set the profit equal to zero. The profit formula is P = Revenue - Cost. Setting the profit equal to zero, we have:
0 = Revenue - Cost
Substituting the revenue and cost equations we derived earlier, we get:
0 = $15x - ($55 + $4x)
Simplifying the equation, we have:
0 = $15x - $55 - $4x
Combining like terms, we get:
0 = $11x - $55
Now, solving for x, the number of pizzas sold, we have:
$11x = $55
x = $55 / $11
x = 5
This means that 5 pizzas must be sold to break even. This means you neither make a profit nor a loss. If you sell fewer than 5 pizzas, you will experience a loss. If you sell more than 5 pizzas, you will make a profit.
d. To determine the profit if 500 specialty pizzas are sold, we can use the profit formula:
Profit = Revenue - Cost
Revenue = Price per pizza * Number of pizzas sold
Cost = Fixed Cost + Labor Cost per pizza * Number of pizzas sold
In this case, the number of pizzas sold is 500. Substituting the values into the equations, we have:
Revenue = $15 * 500 = $7500
Cost = $55 + $4 * 500 = $55 + $2000 = $2055
Profit = $7500 - $2055 = $5445
Interpretation: The profit from selling 500 specialty pizzas is $5445.
e. To determine the number of pizzas needed to make a profit of $1,100, we can rearrange the profit formula:
Profit = Revenue - Cost
Profit + Cost = Revenue
Revenue = Profit + Cost
In this case, the profit is $1,100. Substituting this value into the equation, we have:
Revenue = $1,100 + $55 + $4x
Setting this equal to the price per pizza times the number of pizzas sold, we have:
$15x = $1,100 + $55 + $4x
Simplifying the equation, we have:
$11x = $1,155
x = $1,155 / $11
x ≈ 105
Interpretation: To make a profit of $1,100, approximately 105 specialty pizzas need to be sold.
f. To determine the number of pizzas needed to make a profit greater than $1,595, we can follow a similar process as in part e. Let's call the number of pizzas needed "y". The equation becomes:
$15y > $1,595 + $55 + $4y
Simplifying the equation, we have:
$11y > $1,650
y > $1,650 / $11
y > 150
Interpretation: To make a profit greater than $1,595, more than 150 specialty pizzas need to be sold.