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Homework answers / question archive / The inventor of a new game believes that the variable cost of producing the game is $1
The inventor of a new game believes that the variable cost of producing the game is $1.95$1.95 per unit. The fixed cost is $7800.$7800.
(a) Express the total cost CC as a function of x,x, the number of games sold.
(b) Find a formula for the average cost per unit ¯C=CxC¯=Cx.
(c) The selling price for each game is $5.95.$5.95. How many units must be sold before the average cost per unit falls below the selling price?
a)
Total cost is the sum of the fixed cost and the variable costs. The fixed costs are given as $7800 and the per unit variable costs are $1.95.
The variable costs of producing x units will be 1.95x1.95x.
As the total costs are the sum of the variable costs and the fixed cost, the cost function will be:
C(x)=7800+1.95xC(x)=7800+1.95x
b)
The average cost per unit function will be the cost function divided by the number of units produced, xx
Therefore,
¯C=7800+1.95xx=7800x−1+1.95C¯=7800+1.95xx=7800x−1+1.95
c)
We need to find the value of x such that ¯C<5.95C¯<5.95
We can solve as follows.
7800x−1+1.95<5.957800x<4x>19507800x−1+1.95<5.957800x<4x>1950
Therefore, the average costs fall below $1.95 when 1951 units are produced.
