The DiMonte Corporation invented a new type of sunglass lens. Their variable expenses are $12.66 per unit, and their fixed expenses are $111,200. a. How much does it cost them to produce one lens? 15,000 lenses? b. Express the expense function algebraically. What is the slope of the expense function? c. If the slope is interpreted as a rate, give the units to use. d. What is the average cost, to the nearest cent, of producing 15,000 lenses? e. What is the average cost, to the nearest cent, of producing 17,000 lenses? f. As the number of lenses increased from 15,000 to 17,000, did the average expense per lens increase or decrease?

a) one lens: 111,212.66

15000 lenses: 301,100

b) y=111,200+12.66x

slope: 12.66

c) 12.66 dollars per unit of lens produced

d) 20.07

e) 19.2

f) decreases

Step-by-step explanation:

a) Cost of producing one lens

fixed expenses+variable expenses=111,200+12.66=111,212.66

Cost of producing 15,000 lenses

fixed expenses+variable expenses=111,200+12.66 (15,000) = 301,100

b) Expense function:

let y be the expense cost

let x be the number of lenses produced

y=111,200+12.66x

Slope:

The function is a line equation: y=mx+b where m is the slope.

In this case b=111,200 and m=12.66. So the slope is 12.66

c) the cost increases 12.66 dollars per unit of lens produced

d) The cost of producing 15000 lenses is:

111,200+12.66 (15,000) = 301,100

If DiMonte produces 15000 lenses, the average cost per lens is:

301,100/15000=20.073≈20.07

e) The cost of producing 17000 lenses is:

111,200+12.66 (17,000) = 326,420

If DiMonte produces 17000 lenses, the average cost per lens is:

326,420/17,000=19.2

f) The average per lens decrease.