The total cost (in hundreds of dollars) to produce xx units of a product is C(x)=5x−69x+5C(x)=5x−69x+5

Given Data:

• The total cost of product is: C(x)=5x−69x+5C(x)=5x−69x+5

(b)

The quantity of product is: xunitxunit

The average cost is total cost divide by the number of units of product

The expression for average cost of product of xunitxunit is

Caverage(x)=C(x)xCaverage(x)=C(x)x

Substitute the value and solve the above expression

Caverage(x)=5x−69x+5x=5x−6x(9x+5)=5x−69x2+5x??(I)Caverage(x)=5x−69x+5x=5x−6x(9x+5)=5x−69x2+5x??(I)

Thu the average cost of xunitxunit is 5x−69x2+5x5x−69x2+5x

(a)

• The quantity of product is: x=30unitx=30unit

Substitute the value and solve the expression (I)

Caverage(30)=5(30)−69(30)2+5(30)=150−69(900)+150=0.01811dollarCaverage(30)=5(30)−69(30)2+5(30)=150−69(900)+150=0.01811dollar

Thus the average cost of product for 30units30units is 0.01811dollar0.01811dollar

(c)

Differentiate the expression (I)

d(Caverage(x))dx=d(5x−69x2+5x)dx=(9x2+5x)d(5x−6)d−(5x−6)d(9x2+5x)d(9x2+5x)2=(9x2+5x)(5)−(5x−6)(18x+5)(9x2+5x)2=−45x2+108x+30d(Caverage(x))dx=d(5x−69x2+5x)dx=(9x2+5x)d(5x−6)d−(5x−6)d(9x2+5x)d(9x2+5x)2=(9x2+5x)(5)−(5x−6)(18x+5)(9x2+5x)2=−45x2+108x+30

Thus the marginal average cost function is −45x2+108x+30