A shop buys tablets from the manufacturer for $102 each, and sells them tothe public for $180 each. The shop has fixed costs of $35,000.

Question

a. create an equation that expresses the business' profit as a function of the number of tablets sold.

b. use this equation to determine how many tablets must be sold in order for the shop to break.

Answer 1

Let T=#tablets sold

To find out how much money is made on the sale of each tablet subtract the purchase cost from the sale price.

The amount of money made from each tablet is (180-102)T = 78T

Thus, with operating costs of $35000, our profit function is:

 

P(T) = 78T - 35000

 

To break even we would have profit of zero or:

P(T)=0

To make an actual profit we need P(T)>0

 

 

78T-35000≥0

78T ≥ 35000

T ≥ 35000/78

T ≥ 448.7

 

To make a profit we must sell at least 449 tablets.

 

Lets see what that means.  If we sell 448 tablets we have  

P(T) = 78(448)- 35000 = -56.   This means we have lost $56

 

If we sell 449 tablets P(T)= 78(449)-35000= 22

To make a profit we must sell at least 449 tablets, giving a minimum profit of $22