I just need the answer for number 7 and 8. Thanks!
An oil spill has fouled 200 miles of Pacific shoreline. The company responsible has been ardered to clean the mess. Each clean-up crew costs $16000 to bring in, and $500 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. Your group has been hired by the company to determine how many crews the company should hire ta minimize their costs. 1. Find an equation that gives the cost, Cof cleanup in terms of the number of crews, xhired C'(a) - 16000x + 700000 600000 100000+ 16000 Hint: Start by writing the equation for cost in terms of two variables, crews and days needed for cleanup. Then create a second equation for days needed in terms of crews, and substitute into the first equation. Since 1 crew can clean 1 mile in 1 day, then x crews can clean x miles in 1 day. Then ta clean 200 miles, it 200 will require days Question 2 Score on last try: 3 of 3 pts. See Details for more. You can retry this question below 2. Find the derivative of the cost equation 600000 + 16000 vo Submit Question Question 3 Score on last try: 6.75 of 9 pts. See Details for more. You can retry this question below 3. Determine the number of crews that should be brought in to minimize the cost to the company. a. Mathematically, the number of crews would be: 5V Give the mathematical answer to at least two decimal places. b. Since partial crews cannot be brought in the whole number of crews that should be brought in to minimize cost the company would be: C. The minimum cost to the company (using your answer from 3b) will be: $3755.10 296000 Note: The answer to 3b may not be as simple as rounding the answer to 3a. You should check the actual cast to the company to the whole numbers above and below your answer to Ja. Hint: Set the derivative equal to zero and solve You can retry this question below Now we're going to consider the scenario from another perspective. For questions 5 - 9 of the project, imagine that you are a government EPA analyst, trying to determine the fine-per-day to impose upon the company. Knowing that the company will want to minimize their costs, by adjusting the fine-per-day you can affect what number of crews will be in the company's best interest to bring in. This in turn will affect the number of days taken for cleanup. 5. Rewrite your equation from above, replacing the $3000 fine with the constant f. Your equation will involve both the variable x and the constant f 200 C(x) = 16000x + 100000+ f 2 Submit Question Question 6 Score on last try: 3.6 of 6 pts. See Details for more. 6. Determine the number of crews that should be brought into minimize the cost to the company as a function of the fine amount. crews(f) 5 20 200. f 16000 Question 7 7. Suppose the governments wants the spill cleaned up sooner. Find the amount of fine needed to motivate the company to clean up the spill in: a) 2 weeks. Fine needed: $ per day b) 1 weeks. Fine needed: $ per day c) 3 days. Fine needed: $ per day Note: In each case, presume that only whole numbers of crews can be brought in. If cleaning the spill in the time indicated would require a fractional number of crews, round up to the next whole number of crews so the spill will get cleaned within the time specified. Give answers to the nearest dollar. Question 8 8. As an EPA analyst, you decide to do more calculations using the Cost function found in #5 and the information found in #7. 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? a) 2 weeks. Cost to the company: $ b) 1 weeks. Cost to the company: $ c) 3 days. Cost to the company: $ Note: As in the question, in each case, presume that only whole numbers of crews can be brought in. If cleaning the spill in the time indicated would require a fractional number of crews, round up to the next whole number of crews so the spill will get cleaned within the time specified. Give answers to the nearest dollar. Submit Question An oil spill has fouled 200 miles of Pacific shoreline. The company responsible has been ardered to clean the mess. Each clean-up crew costs $16000 to bring in, and $500 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. Your group has been hired by the company to determine how many crews the company should hire ta minimize their costs. 1. Find an equation that gives the cost, Cof cleanup in terms of the number of crews, xhired C'(a) - 16000x + 700000 600000 100000+ 16000 Hint: Start by writing the equation for cost in terms of two variables, crews and days needed for cleanup. Then create a second equation for days needed in terms of crews, and substitute into the first equation. Since 1 crew can clean 1 mile in 1 day, then x crews can clean x miles in 1 day. Then ta clean 200 miles, it 200 will require days Question 2 Score on last try: 3 of 3 pts. See Details for more. You can retry this question below 2. Find the derivative of the cost equation 600000 + 16000 vo Submit Question Question 3 Score on last try: 6.75 of 9 pts. See Details for more. You can retry this question below 3. Determine the number of crews that should be brought in to minimize the cost to the company. a. Mathematically, the number of crews would be: 5V Give the mathematical answer to at least two decimal places. b. Since partial crews cannot be brought in the whole number of crews that should be brought in to minimize cost the company would be: C. The minimum cost to the company (using your answer from 3b) will be: $3755.10 296000 Note: The answer to 3b may not be as simple as rounding the answer to 3a. You should check the actual cast to the company to the whole numbers above and below your answer to Ja. Hint: Set the derivative equal to zero and solve You can retry this question below Now we're going to consider the scenario from another perspective. For questions 5 - 9 of the project, imagine that you are a government EPA analyst, trying to determine the fine-per-day to impose upon the company. Knowing that the company will want to minimize their costs, by adjusting the fine-per-day you can affect what number of crews will be in the company's best interest to bring in. This in turn will affect the number of days taken for cleanup. 5. Rewrite your equation from above, replacing the $3000 fine with the constant f. Your equation will involve both the variable x and the constant f 200 C(x) = 16000x + 100000+ f 2 Submit Question Question 6 Score on last try: 3.6 of 6 pts. See Details for more. 6. Determine the number of crews that should be brought into minimize the cost to the company as a function of the fine amount. crews(f) 5 20 200. f 16000 Question 7 7. Suppose the governments wants the spill cleaned up sooner. Find the amount of fine needed to motivate the company to clean up the spill in: a) 2 weeks. Fine needed: $ per day b) 1 weeks. Fine needed: $ per day c) 3 days. Fine needed: $ per day Note: In each case, presume that only whole numbers of crews can be brought in. If cleaning the spill in the time indicated would require a fractional number of crews, round up to the next whole number of crews so the spill will get cleaned within the time specified. Give answers to the nearest dollar. Question 8 8. As an EPA analyst, you decide to do more calculations using the Cost function found in #5 and the information found in #7. 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? a) 2 weeks. Cost to the company: $ b) 1 weeks. Cost to the company: $ c) 3 days. Cost to the company: $ Note: As in the question, in each case, presume that only whole numbers of crews can be brought in. If cleaning the spill in the time indicated would require a fractional number of crews, round up to the next whole number of crews so the spill will get cleaned within the time specified. Give answers to the nearest dollar. Submit
