Thread: 2 problem solving questions

1. A real-state firm owns the Parklane Garden Apartments, which consists of 96 apartments. At $550 per month, every apartment can be rented. However, for each $25 per month increase, there will be three vacancies with no possibility of filling them. The firm wants to recieve $54,600 per month from rents. What rent should be charged for each apartment?

2. A health clinic has a solution of bleach to sterilize petri dishes in which culture are grown. The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water. Now research indicated that concentration of bleach should be %5 for complete sterilisation. How much of the solution should be drain and replaced with bleach content to the recommended level?

Originally Posted by johntuan

1. A real-state firm owns the Parklane Garden Apartments, which consists of 96 apartments. At $550 per month, every apartment can be rented. However, for each $25 per month increase, there will be three vacancies with no possibility of filling them. The firm wants to recieve $54,600 per month from rents. What rent should be charged for each apartment?

Not getting too fancy about it, but you start with a base rent of $550 and have 96 apartments. So the total income is which is $1800 short of expectations.

So by increasing the rent by $25 we lose 3 apartments. So the income may be calculated by:

where n is the number of $25 steps the rent has increased by. Numerically we have:


Since we need an income of $54600 we will need:

or






Thus n = 4 or 6.

So we are using either 4 steps of $25 or 6 steps of $25. Which value should you choose? I'll leave that one open to the more business minded people than me.

-Dan

Originally Posted by johntuan

2. A health clinic has a solution of bleach to sterilize petri dishes in which culture are grown. The sterilization tank contains 100 gal of a solution of 2% ordinary household bleach mixed with pure distilled water. Now research indicated that concentration of bleach should be %5 for complete sterilisation. How much of the solution should be drain and replaced with bleach content to the recommended level?

In every 100 gal of 2% solution there are 2 gal of pure bleach. We wish to remove some number of gallons x of solution and replace it with x gal of pure bleach, such that the solution concentration is 5%.

So we have 100 - x gal of 2% solution + x gal bleach which gives us the 5% solution. By volume this will give 100 gal of 5% solution, so we expect there to be a total of 5 gal of pure bleach.

In 100 - x gal of 2% solution there are 0.02(100 - x) gal of pure bleach. So:






gal

So we need to remove 3.0612 gal of the 2% solution and replace it with 3.0612 gal of pure bleach.

-Dan

Originally Posted by topsquark

So we are using either 4 steps of $25 or 6 steps of $25. Which value should you choose? I'll leave that one open to the more business minded people than me.

-Dan

Ive gotten everything that you have said but what do i do now? Do I take 4*25 or 6*25 then add it to the rent and thats my answer?

Originally Posted by johntuan

Ive gotten everything that you have said but what do i do now? Do I take 4*25 or 6*25 then add it to the rent and thats my answer?

Yup!

So the rent will either be $650 or $700 depending on how many empty apartments the place wants.

-Dan

thanks for your help. Imo it would make more business sense to charge $650 per month since you are housing more people.Thus, you can make more profits if you increase the rent. I could be wrong though.