Math Differentiation problem

[Arsen]

A car rental agency rents 180 cars per day at a rate of $30 per day. For each $1 increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income and what is the maximum income?

 

(I know the answer but I do not know how to get it so can someone please show me step by step the putting this question from words into numbers and some formula to get the answer)

[Guest Generallee]

Sorry to sound harsh but this is a tech forum, we're not here to do your homework.

[wng_kingsley7]

A car rental agency rents 180 cars per day at a rate of $30 per day. For each $1 increase in the daily rate, 5 fewer cars are rented. At what rate should the cars be rented to produce the maximum income and what is the maximum income?

 

(I know the answer but I do not know how to get it so can someone please show me step by step the putting this question from words into numbers and some formula to get the answer)

Pick out the information that is most important; (then re-arrange them in different formulae to solve it)

• Rents out 180 cars per day for $30 = total of $560
• If you constantly add $1 per day on the daily rate of $30 you'll only be renting cars for the next 36 days (excluding the first day which is day 0) in total 37 days. 180/5=36
•  

I think there is a issue with the wording at the end of your question & how influx are the daily rates? If not not gonna lie I got totally baffled #ROFL when you forget who to approach theory mathematics :wacko: What is the answer you came to a conclusion to? Please explain.

 

Sorry to sound harsh but this is a tech forum, we're not here to do your homework.

Well it's off-topic & a maths challenge is always fun to solve. Though it looks like you lack the enthusiasm to solve it then I guess it's just a blundered thread.

[Arsen]

Pick out the information that is most important; (then re-arrange them in different formulae to solve it)

• rents out 180 cars per day for $30 = total of $560

I think there is a issue with the wording at the end of your question & how influx are the daily rates? If not not gonna lie I got totally baffled #ROFL when you forget who to approach theory mathematics :wacko: What is the answer you came to a conclusion to? Please explain.

 

Well it's off-topic & a maths challenge is always fun to solve. Though it looks like you lack the enthusiasm to solve it then I guess it's just a blundered thread.

The answer to the question is $33 and max profit is $5445 but I dont know another way to get it other than keep guessing with $31 and $32 and so on till you reach a peak and it begins decreasing. Then I know the max profit is the number before that. But there must be a formula to get it I just forgot how to get the formula. Basically it is saying each time you increase the price of each car by $1 the number of cars rented that day decrease by 5. So if the price was set for $31 the amount of cars they would rent that day would be 175 giving them a profit of $5425.

[Virgule]

[Arsen]

My hero <3

[juretrn]

Nvm

[Virgule]

My hero <3

Try to apply this methodology to other problems. 

 

Always rephrase the problem in terms of equations. That's the first step. Then try and comprehend what you need to find. In this case, remember that polynomial functions have minimum and maximum values when their differential equals 0.

 

 GO...MY SON... GO PRACTICE

[juretrn]

Damnit I got confused.. I guess this was too easy after trying to chew through partial differential equations, Laplace transforms, functionals etc in the last few weeks:(

[Virgule]

partial differential equations, Laplace transforms, functionals 

Nothing of that sort here (wtv functionals are).

[Arsen]

Try to apply this methodology to other problems. 

 

Always rephrase the problem in terms of equations. That's the first step. Then try and comprehend what you need to find. In this case, remember that polynomial functions have minimum and maximum values when their differential equals 0.

 

 GO...MY SON... GO PRACTICE

Everything else I know and is simple for me I only find it hard to rephrase the problem into terms of equations

[Virgule]

Everything else I know and is simple for me I only find it hard to rephrase the problem into terms of equations

Start by setting variables.

 

You need to find the optimal number of cars that yields the highest income.  Right there I mentioned 2 variables. Also, when you think of it, both are function of the rate, which needs to be the third variable. Since both are functions of the same variable, the income can be expressed in terms of the rate ALONE. 

 

There you go, you have your equations. Now what do you need to find ? The maximal income right ? That means where the differential equals 0. The rest is just simple math and verification.

[Arsen]

Start by setting variables.

 

You need to find the optimal number of cars that yields the highest income.  Right there I mentioned 2 variables. Also, when you think of it, both are function of the rate, which needs to be the third variable. Since both are functions of the same variable, the income can be expressed in terms of the rate ALONE. 

 

There you go, you have your equations. Now what do you need to find ? The maximal income right ? That means where the differential equals 0. The rest is just simple math and verification.

Appreciate the help

[Guest Generallee]

Well it's off-topic & a maths challenge is always fun to solve. Though it looks like you lack the enthusiasm to solve it then I guess it's just a blundered thread.

 

I know it's off topic but there are thousands of math forums around just for that, but you're right i hate maths so i lack the enthusiasm to solve it

 

Well, i've seen worse, it's not like those pussies with their friendzone threads. I can't stand those. 

[Virgule]

I know it's off topic but there are thousands of math forums around just for that, but you're right i hate maths so i lack the enthusiasm to solve it

 

Well, i've seen worse, it's not like those pussies with their friendzone threads. I can't stand those. 

k

[wng_kingsley7]

I know it's off topic but there are thousands of math forums around just for that, but you're right i hate maths so i lack the enthusiasm to solve it

 

Well, i've seen worse, it's not like those pussies with their friendzone threads. I can't stand those. 

Everyone has an opinion they may or may not like to share. Maths isn't my forte either so yeah :wacko: