Hi need help please thank you very muuch

[Guest]

[quote][/quote]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.

[Guest]

Where did you get this problem? It appears to be a problem from a class but you don't seem to understand what these words mean!

You are told that "the demand for this new product is given by the equation q = 345 - 0.5p."

You are told that "T-+he company also believes that the variable costs for 100 pencils are 5q-10[/quote]
This makes no sense. The "costs for 100 pencils" cannot be a function of q, the number of pencils!
I am going too assume that"the variable costs for q pencils is 5q- 10".

"and the fixed costs for all production are $3,000."
The total costs are the variable costs plus the fixed costs: 5q- 10+ 3000= 5q+ 2990.

"(a) Determine income based on quantity q."

Income is the number sold times the price of each. If you sell 100 pencils to $0.10 each then your income is \$100*0.10= \$10. So, here, the income is pq. You know q as a function of q, q= 345- 0.5p so, since you want "income based on quantity q", you need to solve that for p as a function of q: q- 345= -0.5p, p= (q- 345)/(-0.5)= -2(q- 345)= -2q+ 690. Then pq= (-2q+ 690)q= 690q- 2q^2.

"(b) Determine the profit of the business based on q."
Profit is income minus costs.