Question

a) a farmer sells cabbages for N$ 10 per head. The farmers variable costs are N$ 2.50 per head and total cost of 100 heads is N$1450.

I) how many cabbages must the manufacturer produce each month to break even?

II) how many cabbages should be produced to make profit

b) Total cost of producing carrot is C(X)=3600+100x+2x^2 and the total revenue function R(x)= 500x-2x^2

I) find the number of kg that maximizes profit

II) find maximum profit

Answer 1

a)

i

Given

Price = 10

Variable cost = 2.50

Total cost of 100=1450

Break even point

$TC=TR\\ 1450=10Q\\ Q=145$

ii

We know that

$TC=VC+FC\\ 1450=(2.50\times 100)+FC\\ 1450=250+FC\\ FC=1200$

Inorder to make profit 161 cabbages must be produced.

$P=TR-TC\\ P=(10\times 161)-(1200+(161\times 2.5))=7.5$

b)

i

$TR=TC\\500x-2x^2=3600+100x+2x^2\\4x^2-400x+3600=0\\4 ( 𝑥 ^2 − 1 0 0 𝑥 + 9 0 0 ) = 0\\x=10\\x=90$

90kg

ii

profit

$=price\times quantity\\90\times 7.5=675$