If the fine imposed is the one needed to motivate the company to cleanup the spill in the specified number of days, and the company hires crews to do that, what would the Cost to the company be?

Question

WHAT YOU KNOW:

An oil spill has fouled 400 miles of Pacific shoreline. The company responsible has been ordered to clean the mess. Each clean-up crew costs $14000 to bring in, and $400 per crew per day. Each crew can clean 1 mile of shoreline per day. To encourage a speedy cleanup, the government is levying a fine of $3000 per day against the company.



The minimum amount of crew is 9

"f": the constant from $3000

Cost Equation: C(x) = 160000 +14000x + (400f)/x

Fine needed in 2 weeks --> $29435

Fine needed in 1 weeks --> $117740

Fine needed in 3 days ---> $628460

What you need to SOLVE:

a) 2 weeks. Cost to the company: $_____

b) 1 weeks. Cost to the company: $_____

c) 3 days. Cost to the company: $_____

Answer 1

a)

To = complete the job in two weeks, 14 days, 29 crews are needed (400 / 14 = 28.571)

C = $160000 + (29)($140000) + (14)($3000)

b)

To complete the job is one week, 7 days, 58 crews are needed (400 / 7 = 57.142)

C = $160000 + (58)($14000) + (7)($3000)

c)

To complete the job in 3 days, 134 crews are needed (400 / 3 = 133.333)

C = $160000 + (134)($14000) + (3)($3000