Question

A farmer sells cabbages for N$10 per head. The farmer’s 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? (6)
ii. How man cabbages should be produced to make profit (4)
b) Total cost of producing carrots is C(x) = 3600+100x+2x2
and the total revenue function
R(x) =500x-2x2
i. Find the number of kg that maximizes profit (6)
ii. Find maximum profit

Answer 1

(a)

(i)

VC=2.50

TC=14.50

Contribution Margin = price of product- variable cost.

Contribution Margin=10-2.50=7.50

Total cost per unit =$\frac{1450}{100}=14.50$

Fixed cost per unit $= 14.50-2.50=12.50$

Break even $=\frac{12.50}{7.50}=1.67$

This implies that for approximately 2 cabbages should be produced to break even.

(ii)

In order to make profit, the units of cabbage produced should be more than two.

(b)

(i)

TC: $C(X)=3600+100x+2x^2$

TR: $R(X)=500x+2x^2$

$MC=100+4x$

$MR=500-4x$

At maximum profit, $MC=MR$

$100+4x=500-4x$

$x=50$

No.of kgs that maximizes profit =50.

(ii)

Maximum profit= total revenue- total cost.

$TC= 3600+100(50)+2(50^2)=13600$

$TR= 500(50)-2(50^2)=30000$

Maximum profit $=30000-13600=16,400$