A souvenir shop sells about 200 coffee mugs each month for 6$ each. The shop owner estimates that for each $0.50 increase in the price, he will sell about 10 fewer coffee mugs per month.
a. How much should the owner charge for each mug in order to maximize the monthly income from their sales?
b. What is the maximum monthly income the owner can expect to make from the mugs?
I've been working on this for around 2 or 3 hours now, its one of my Homework problems, I really don't understand it :/ It'd be extremely appreciated if you could show me how to do it. (Work included as I get confused when teachers jump from one place to another)
5 answers
NOTE: I already have the function and what x equals which is 4, though I don't know where to go from there :/
It would surely help if you showed how you got there. What you provide is not much help.
If x is the number of price increases, then we have
price p = 6.00 + 0.50x
quantity sold q = 200 - 10x
revenue is price * quantity, so
r(x) = (6.00 + 0.50x)(200-10x)
= 1200+40x-5x^2
This is just a parabola, with its vertex at x=4, as you say.
So, just figure f(4) to get the maximum income.
If you don't understand it, how did you come up with the 4?
If x is the number of price increases, then we have
price p = 6.00 + 0.50x
quantity sold q = 200 - 10x
revenue is price * quantity, so
r(x) = (6.00 + 0.50x)(200-10x)
= 1200+40x-5x^2
This is just a parabola, with its vertex at x=4, as you say.
So, just figure f(4) to get the maximum income.
If you don't understand it, how did you come up with the 4?
Well, after spending about another hour to half an hour comparing this problem to my notes and the other similar problem on this website I finally came up with my answer.
a. 8$ for each mug
b. 1280$
I came up with the 4 by looking at my notes and the other problem on the website similar to this and setting up the equation
(6+0.50x)(200-10x) letting x = # of price increases.
Then I foiled that out and got -5x^2+40x+1200
Then I used the equation x=-b/2a and got x=4
After that I made this post as I was unsure what to do with the 4. Then I looked at my notes and took a guess and did 4*0.5 and got 2. I then added this 2 to the six from the original problem and got 8 which lead to my answer 8$ for each mug. So 8$ was my answer for a.
Then I saw I still did not have a response to my question and I went ahead and tried b. Since every 0.50 price increase the store lost 10 mugs that meant 4 price increases because you have to add 0.50 to 6 each increase and you wanted to get 8, so 4 0.50 price increases as I said. Then I multiplied 4*10 to get the amount of mugs lost and subtracted it from 200. the original mug amount. This gets me 160 and I multiply it by 8 to get the maximum monthly income the owner can expect to make from the mugs (question b) which is $1280.
Would this be correct?
a. 8$ for each mug
b. 1280$
I came up with the 4 by looking at my notes and the other problem on the website similar to this and setting up the equation
(6+0.50x)(200-10x) letting x = # of price increases.
Then I foiled that out and got -5x^2+40x+1200
Then I used the equation x=-b/2a and got x=4
After that I made this post as I was unsure what to do with the 4. Then I looked at my notes and took a guess and did 4*0.5 and got 2. I then added this 2 to the six from the original problem and got 8 which lead to my answer 8$ for each mug. So 8$ was my answer for a.
Then I saw I still did not have a response to my question and I went ahead and tried b. Since every 0.50 price increase the store lost 10 mugs that meant 4 price increases because you have to add 0.50 to 6 each increase and you wanted to get 8, so 4 0.50 price increases as I said. Then I multiplied 4*10 to get the amount of mugs lost and subtracted it from 200. the original mug amount. This gets me 160 and I multiply it by 8 to get the maximum monthly income the owner can expect to make from the mugs (question b) which is $1280.
Would this be correct?
You are correct.
4 was indeed the solution to the equation, but you correctly went on to realize that that meant the actual price was $8/mug.
Good work.
Still, just plugging x=4 into the equation would have given the same answer for the income, since that accounted for the actual price and quantity.
4 was indeed the solution to the equation, but you correctly went on to realize that that meant the actual price was $8/mug.
Good work.
Still, just plugging x=4 into the equation would have given the same answer for the income, since that accounted for the actual price and quantity.
Thank you (;
Also thanks for the tip on the plugging in 4 ;D
Also thanks for the tip on the plugging in 4 ;D
1 answer