Question

Suppose that you opened a pizzeria. From your experience, you know that if you charge $15 per pizza you will sell 50 pizzas in a day and, if you charge $10 per pizza, you sell 75 pizzas. Furthermore, each pizza costs you $5 to make. Do the following analysis on your sales.

1. Assuming price and demand are related linearly, determine the price demand equation relating price to the number of pizzas sold.

2. Use this to determine revenue (total amount of money taken in) as a function of price sold. For what price(s) will you have 0 revenue?

3. Determine cost as a function of price. For what price(s) will you have 0 cost?

4. Use cost and revenue to determine the profit (net money made) as a function of price. For what price(s) will you have 0 profit?

Answer 1

1.

Since we know that the price and demand are linearly related, then it means that the curve will be A straight line.

Assuming price "p" is on the y axis and quantity produced "q" on the x axis. According to question the price demand line passes through (50,15) and (75,10)

Hence, the demand price function curve will be,

2.

The revenue is the product of the quantity sold and the price per quantity, Assuming all the products amounting to "q" made are sold at price "p" per piece,

We have substituted q in from (1)

For 0 revenue, we equate R to 0,

So at price p=0 or 25 we get zero revenue.

3.

Cost is the amount spent in making the item i.e, pizza

Cost will be zero, when C=0=>p=25

4.

To find when profit will be zero, we have to equate profit to 0,

So for prices 5 and 25 he could have zero profit.