If x represents the number of items produced a write a cost

If x represents the number of items? produced, ?(a) write a cost? function, ?(b) find a revenue function if each item sells for the price? given, ?(c) state the profit? function, ?(d) determine analytically how many items must be produced before a profit is realized? (assume whole numbers of? items), and ?(e) support the results of part? (d) graphically.

Solution

Cost function:

fixed cost = $ 700 .Let no. of items produced be x

C(x) =700 +20x

Revenue function:

R(x) = 45x

Profit = Revenue - Cost

P(x) = 45x - (700 +20x)

= 25x - 700

Breakeven point aftre which profit would be realised :

25x - 700 =0

x = 700/25 = 28 items