1.) You are under contract to design a storage building with a square base and a
ID: 2846840 • Letter: 1
Question
1.) You are under contract to design a storage building with a square base and a volume of 15000 cubic feet. The cost of materials is $5 per square foot for the floor, $15 per square foot for the walls and $5 per square foot for the roof. Find the width of the square base that minimizes the cost of materials. SHOW WORK
2.)American Airlines requires that the total outside dimensions (Length + Width + Height) of your carry on bag not exceed 81 inches.
Suppose you want to buy a carry on bag whose length is twice its height (L = 2H).
What does the height have to be so that the volume of the bag will be maximized? SHOW WORK
3.) The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model:
C(q) = 4400 + 180q2
where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. Government will pay subsides in the amount of $350 per pound for each pound of pollutant removed (q). For example, if you can remove q=3 pounds of pollutant, you will receive a subsidy of $350*3.
How many pounds of pollutant should the firm remove each day in order to minimize Net Cost (Cost minus subsidy)? SHOW WORK
4.)An efficiency study of the first shift (from 8:00 A.M. to 5:00 P.M.) at a certain factory indicates that an average worker who arrives on the job at 8:00 A.M. will have assembled Q(t) = -1t3 + 8t2 + 14t MPEG Players t hours later. How many hours after the start of the shift is the worker performing most efficiently? SHOW WORK
5.)Cowboy Curtis wants to build a dirt road from his ranch to the highway so that he can drive to the city in the shortest amount of time. The perpendicular distance from the ranch to the highway is 6 miles and the city is located 11 miles down the highway. Where should Curtis join the dirt road to the highway if the speed limit is 22 mph on the dirt road and 70 mph on the highway? SHOW WORK
Explanation / Answer
1. In the 1st answer if you refer to my solution, you will get:
C(w) = 10w^2 + 900000/w
dc/dw = 20w - 900000/w^2 = 0
=> 20w^3 = 900000
=> w = 35.37 ft
2. Refer to my answer
We get the equation
V(h) = 2h^2(81-3h)
dV/dh = 324h - 18h^2 = 0
=> h = 324/18 = 18 inch
3. This is correct.
I got the answer as 0.972 pounds or 0.972*100 = 97.2 pounds
5. This answer is correct
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.