Question

A company builds a new wing for its east branch and knows that each additional room will gain $1200 of profit. The construction company will cost $44,000 to construct the wing.

How many rooms are need to break even? (Hint: You must PAY the fee to the construction company.)

If you wanted to make twice as much profit as you spent, how many rooms would need to be built?

Answer 1

a. 37 rooms are need to break even.

b. 73 rooms are required to make twice as much profit as you spent.

Explanation:

Revenue of the company from each additional room is $1200.

Total construction cost = $44,000.

At break even condition, total revenue is equal to total cost. In other words, the profit of the firm is zero at break even.

Let x be the number of rooms that are need to break even.

Total revenue of x room is

`TR=1200x`

At break even,

Total revenue = Total cost

`1200x=44000`

Divide both sides by 1200.

`x=(44000)/(1200)=36.6667\approx 37`

Therefore, 37 rooms are need to break even.

Let y be the number of rooms to make twice as much profit as you spent.

Total revenue of y room is

`TR=1200y`

Total revenue = 2 × Total cost

`1200x=2* 44000`

`1200x=88000`

Divide both sides by 1200.

`y=(88000)/(1200)=73.33\approx 73`

Therefore 73 rooms are required to make twice as much profit as you spent.