The inventor of a new game believes that the variable cost of producing the game is $1

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.