2. Units cost $0.50 each to produce an item and they sell for $3.00 each. The...
2. Units cost $0.50 each to produce an item and they sell for $3.00 each. The overhead in setting up production is $2,000.
a) Find the cost and the revenue functions.
b) Find the breakeven point. Also graph the cost and revenue functions and label the breakeven point.
c) How many units must be sold to yield a profit of $2,000?
d) Find the average profit function and the rate of change of the average profit when x=20 items.
Homework Answers
a ) COST FUNCTION & REVENUE FUNCTION :
Cost fn. = FC + VC
Lets assume that the number of unit is X,
Given , Set up cost ( fixed cost ) = $ 2,000
VC per unit = $0.5
COST FUNCTION = 2,000 + 0.5X
Revenue fn. = selling price * quantity
Given , selling price = $ 3 per unit
REVENUE FUNCTION = 3X
b ) BREAK EVEN POINT :
BEP = FIXED COST / CONTRIBUTION PER UNIT
CONTRIBUTION PER UNIT = SELLING PRICE / UNIT ( - ) VARIABLE COST / UNIT
Contribution / unit = $ 3 - $ 0.5
= $ 2.5
BEP = $ 2,000 / 2.5
BEP ( UNITS ) = 800 Units
c ) UNITS TO BE SOLD TO EARN PROFIT OF $ 2,000
= FIXED COST + PROFIT TO BE EARNED CONTRIBUTION PER UNIT
= 2,000 + 2,000 / $2.5
= 4,000 / 2.5
= 1,600 UNITS
d ) Average profit function = profit function / X
profit function = revenue function - cost function
= 3X - 0.5X - 2,000
Avg profit function = 3X - 0.5X- 2,000 X
= 3 - 0.5 - 2000/X
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