Hi need your help for this exercise, thank you

[Broyont]

After conducting market research for a new pencil product, ABC Company believes that the demand for this new product is given by the equation q = 345 - 0.5p. Where q is the quantity sold (measured in hundreds of pencils) and p is the price of 100 pencils.
The company also believes that the variable costs for 100 pencils are 5q-10 and the fixed costs for all production are $3,000.
(a) Determine income based on quantity q.
(b) Determine the profit of the business based on q.

 

[Deleted member 4993]

After conducting market research for a new pencil product, ABC Company believes that the demand for this new product is given by the equation q = 345 - 0.5p. Where q is the quantity sold (measured in hundreds of pencils) and p is the price of 100 pencils.
The company also believes that the variable costs for 100 pencils are 5q-10 and the fixed costs for all production are $3,000.
(a) Determine income based on quantity q.
(b) Determine the profit of the business based on q.

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Broyont]

Here is a picture, sorry the exercise is in french but i know u would understand.

 

[Dr.Peterson]

We didn't really need to see the problem again (though it might turn out to be useful). What we need from you is some indication of what help you need. What have you tried? How far did you get? What went wrong?

 

[Broyont]

Hello!

Yes, in picture you can see the steps that i did so to sumerize here's what i did:

q=345-0.5p
q-345= -0.5p................................[edited: - was missing ]
-2q+690= p................................[edited: q was missing ]

So thats my answer for the number A) of the exercise the number B) im fine but its only the A) that im not sure!

 

[Broyont]

Well i think ive figured it out:

So here it is :
Revenue: q*p
Rev: (345-0.5p)*p
Rev: 345p-0,5p2

 

[Dr.Peterson]

Yes, in picture you can see the steps that i did so to sumerize here's what i did:

q=345-0.5p
q-345= -0.5p................................[edited: - was missing ]
-2q+690= p................................[edited: q was missing ]

So thats my answer for the number A) of the exercise the number B) im fine but its only the A) that im not sure!

Sorry, since it was in French, and you didn't explain, I didn't look closely enough to see that it was your work (for part a), not just the problem.

Well i think ive figured it out:

So here it is :
Revenue: q*p
Rev: (345-0.5p)*p
Rev: 345p-0,5p2

I think when you are asked for "income based on quantity q", that means income as a function of q. You wrote it here as a function of p.

As you have realized, the income (or revenue) is pq, so you just need to multiply the variable q by the expression for p that you had previously.