Please help me to solve this 10 problems step by step, Thank you!

12. [0/1 Points] PREVIOUS ANSWERS SCALCCCS 4.6.019. PRACTICE ANOTHER A rectangular storage container without a lid is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $15 per square meter. Material for the sides costs $9 per square meter. Find the cost (in dollars) of materials for the least expensive such container. (Round your answer to the nearest cent.) $ .450 x Enhanced Feedback Please try again, keeping in mind that the volume of an open box with height h and a rectangular base whose length is twice its width w is V = szh, and the cost function of its surface is C = c1(2w2) + cz[2(wh) + 2(2wh)], where C1 is :the cost for the base and c2 is the cost for the sides. Find a relationship between w and h, using the fact that the volume is a constant. Rewrite the cost function as a function of one variable. Use calculus to nd the minimum possible cost. Need Help? 6. [0/1 Points] DETAILS PREVIOUS ANSWERS SCALCCC5 4.6.059.MI. MY NOTES PRACTICE ANOTHER An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to be constructed from the refinery to storage tanks located on the south bank of the river 6 km east of the refinery. The cost of laying pipe is $200,000/km over land to a point P on the north bank and $400,000/km under the river to the tanks. To minimize the cost of the pipeline, how far (in km) from the refinery should P be located? (Round your answer to two decimal places.) * km Need Help? Read It Master It Submit Answer 7. [-/2 Points] DETAILS SCALCCC5 4.6.015. MY NOTES PRACTICE ANOTHER A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be (in ft) in order to minimize the cost of the fence? smaller value ft larger value ft Need Help? Read It Submit Answer 8. [-/1 Points] DETAILS SCALCCC5 4.6.018.MI. MY NOTES PRACTICE ANOTHER If 30,000 cm of material is available to make a box with a square base and an open top, find the largest possible volume (in cm ) of the box. cm Need Help? Read It Master It Submit Answer3. [-/2 Points] SCALCCCS 4.6.042. PRACTICE ANOTHER The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. If the area of printed material on the poster is fixed at 1,536 cmz, find the dimensions (in cm) of the poster with the smallest area. width cm height cm 4. [-I1 Points] SCALCCCS 4.6.011. PRACTICE ANOTHER The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function 120! P= 12+I+9 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum? I = :] thousand foot-candles Need Help? noun Submit Answer 5. [-/2 Points] DETAILS SCALCCCS 4.6.070. PRACTICE ANOTHER During the summer months Terry makes and sells necklaces on the beach. Last summer she sold the necklaces for $10 each, and her sales averaged 20 per day. When she increased the price by $1, she found that the average decreased by two sales per day. (a) Find the demand function (price p as a function of units sold x), assuming that it is linear. W) = (b) If the material for each necklace costs $8, what selling price should Terry set to maximize her profit? $ I per necklace PRACTICE ANOTHER A farmer wants to fence in a rectangular plot of land adjacent to the north wall of his barn. No fencing is needed along the barn, and the fencing along the west side of the plot is shared with a neighbor who will split the cost of that portion of the fence. If the fencing costs $24 per linear foot to install and the farmer is not willing to spend more than $6000, nd the dimensions for the plot that would enclose the most area. (Enter the dimensions as a comma 9. [-11 Points] SCALCCC5 4.6.021. separated list.) f Need Help? |m Submit Answer 10. [-/1 Points] DETAILS SCALCCC5 4.6.072. MY NOTES PRACTICE ANOTHER A company operates 16 oil wells in a designated area, Each pump, on average, extracts 272 barrels of oil daily. The company can add more wells, but every added well reduces the average daily output of each of the wells by 8 barrels, How many wells should the company add in order to maximize daily production? wells Need Help? Submit Answer 1. [0/1Points] I DETAILS ll PREVIOUSANSWERS I SCALCCC54.6.041.MI. A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle, labeled x.) ixi Q) If the perimeter of the window is 32 feet, find the exact value of X (in ft) so that the greatest possible amount of light is admitted. X= ft X