A fence must be built to enclose a rectangular area of 45,000 ft. Fencing material costs $4 per foot for the two sides facing north and south and $8 per foot for the other two sides. Find the cost of the least expensive fence. . . . The cost of the least expensive fence is $. (Simplify your answer.) Determine the average cost function C(x) = ~(X) . To find where the average cost is smallest, first X calculate C'(x), the derivative of the average cost function. Then use a graphing calculator to find where the derivative is 0. Check your work by finding the minimum from the graph of the function C (x ) . C(x) = _x3 +4x2 - 2x + 30 If the price charged for a candy bar is p(x) cents, then x thousand candy bars will be sold in a certain city, where p(x) = 169 - X 10 a. Find an expression for the total revenue from the sale of x thousand candy bars. b. Find the value of x that leads to maximum revenue. c. Find the maximum revenue. A local club is arranging a charter flight to Hawaii. The cost of the trip is $542 each for 84 passengers, with a refund of $5 per passenger for each passenger in excess of 84. a. Find the number of passengers that will maximize the revenue received from the flight. b. Find the maximum revenue. A rectangular tank with a square base, an open top, and a volume of 5324 ft is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. . . The dimensions of the tank with minimum surface area are|ft. (Simplify your answer. Use a comma to separate answers.) A closed box with a square base is to have a volume of 85,750 cm". The material for the top and bottom of the box costs $5.00 per square centimeter, while the material for the sides costs $2.50 per square centimeter. Find the dimensions of the box that will lead to the minimum total cost. What is the minimum total cost?A restaurant has an annual demand for 902 bottles of California wine. It costs $2 to store 1 bottle for 1 year, and it costs $10 to place a reorder. (a) Find the optimum number of bottles per order. (b) How many times a year should the wine be ordered? Suppose that in the inventory problem, the storage cost depends on the maximum inventory size, rather than the average. In this case. the number of units that should be ordered or manufactured ml to minimize the total cost is q = T' A book publisher wants to know how many times a year a print run should be scheduled. Suppose it costs $1400 to set up the printing process, and the subsequent cost per book is so low it can be ignored. Suppose further that the annual warehouse cost is $6 times the maximum number of books stored. Assuming 5700 copies of the book are needed per year, how many books should be printed in each print run? The publisher should print |:| books in each print run. (Type a whole number.) For the following demand tunction. nd a. E, and b. the values ofd (if any) at which total revenue is maximized. q = 37,400 sp2 Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the demand elastic, inelastic, or neither at the indicated values? q = 403 0.2p2 a. $24 b. $36 Find the absolute extrema if they exist, as well as ail values of x where they occur, for the function f()() = 2x3 + 8x2 + 8x +1 on the domain [ 5.0]. A manufacturer has a steady annual demand for 3960 cases of sugar. It costs $8 to store 1 case for 1 year. $35 in setup cost to produce each batch, and $15 to produce each case. (.3) Find the number of cases per batch that should be produced to minimize cost. (b) Find the number of batches of sugar that should be manufactured annually. The short-term demand for crude oil in Country A in 2008 can be approximated by q =f(p)=1,883,504p_ 0'03, where p represents the price of crude oil in dollars per barrel and q represents the per capita consumption of crude oil. Calculate and interpret the elasticity of demand when the price is $?8 per barrel. A software entertainment company recently ran a holiday sale on its popular software program. Using data collected from the sale, it is possible to estimate the demand corresponding to various discounts in the price of the software, Assuming that the original price was $36, the demand for the software can be estimated by the function q = 3,251,000p' 1485, where p is the price and q is the demand. Calculate and interpret the elasticity of demand. What formula should be used to compute the elasticity of demand, E, itq is demand at a price p? JAE Cl UP E=q-dp V E: P cI dp dq E=p-dq Find the elasticity of demand. E