Demand fucnction and total cost function....?

Question

A company knows the cost to produce 1000 items is $8000, while the cost to produce 5000 items is $16000.

(a) Find the total cost function given that it is linear.

(b) If the items sell for $4.00 each, what is the break-even point/quantity?

(c) If the demand function is q = 4000 - 200p and the Total Cost function is as in (a), what quantity will maximise the profit? What is the corresponding price and profit?

Answer 1

y=a.x+b is equation of linear function

(a) Y=2X+6000 where Y is total cost and X is quantity (number items produced) and 6000 is fixed costs and a=$2 is variable cost per one item produced

(b) 4X = 2X + 6000 => 3000 items

(c)

spreadsheet:

price/sales rev/ quantity/cost/profit

11/19800/1800/9600/10200

1800 items sold at $11 for max profit of $10200