Question

An office supply store purchased a case of binders for $600. The profit (P) to be made on the binders is defined by the function

P(b) - 8.50b - 600, where b is the number of binders sold.
Part A What is the range of the function if the domain is {10, 45, 72, 100)?
Part B What do the domain and range represent in this situation?
Part C What is the minimum number of binders that the store needs to sell in order to make a profit (P >0)? Show or explain your work.
Part D What is the minimum profit the store can make on the sale of these binders? Show or explain your work.

Answer 1

Part A

Domain = input values

Range = output values

Therefore, if the domain is {10, 45, 72, 100} then input those values into the function:

P(10) = 8.50(10) - 600 = -515

P(45) = 8.50(45) - 600 = -217.5

P(72) = 8.50(72) - 600 = 12

P(100) = 8.50(100) - 600 = 250

So the range is {-515, -217.5, 12, 250}

Part B

The domain is the number of binders sold

The range is the profit in dollars

Part C

Set the function to >0:

⇒ P(b) > 0

⇒ 8.50b - 600 > 0

add 600 to both sides:

⇒ 8.50b > 600

divide both sides by 8.50:

⇒ b > 70.58823529...

Therefore, the minimum number of binders the store needs to sell in order to make a profit is 71.

Part D

If the store sells a minimum of 71 binders, then substitute b = 71 into the function and solve to find the minimum profit:

⇒ P(71) = 8.50(71) - 600

⇒ P(71) = 603.5 - 600

⇒ P(71) = 3.5

Therefore, the store will make a minimum of $3.50 profit if it sells at least 71 binders.

However, if the store sells less than 71 binders, it will make a loss.