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Ever Green Gardening is designing a rectangular compost container that will be twice as tall as it is wide and must hold \(18 \mathrm{ft}^{3}\) of \(\mathrm{com}-\) posted food scraps. Find the dimensions of the compost container with minimal surface area (include the bottom and top).

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, \(R(x),\) and \(\cos t, C(x)\) are in dollars. $$R(x)=50 x-0.5 x^{2}, \quad C(x)=10 x+3$$

Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, \(R(x),\) and \(\cos t, C(x)\) are in dollars. $$R(x)=5 x, \quad C(x)=0.001 x^{2}+1.2 x+60$$

Sketch the graph of cach function. List the coordinates of where extrema or points of inflection occurs State where the function is increasing or decreasing, as well as where it is concave up or concave down. $$f(x)=x^{3}-6 x^{2}+12 x-6$$

Find the absolute maximum and minimum values of each function over the indicated interval, and indicate the \(x\) -values at which they occur. $$f(x)=x^{4}-8 x^{2}+3 ;[-3,3]$$

A university is trying to determine what price to charge for tickets to football games. At a price of 18 dollars per ticket, attendance averages 40,000 people per game. Every decrease of 3 dollars adds 10,000 people to the average number. Every person at the game spends an average of 4.50 dollars on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

Sketch the graph of each function. Indicate where each function is increasing or decreasing, where any relative extrema occur, where asymptotes occur, where the graph is concave up or concave down, where any points of inflection occur, and where any intercepts occur. $$f(x)=x+\frac{9}{x}$$

Find the rates of change of total revenue, cost, and profit with respect to time. Assume that \(R(x)\) and \(C(x)\) are in dollars. \(R(x)=50 x-0.5 x^{2}\) \(C(x)=10 x+3\) when \(x=10\) and \(d x / d t=5\) units per day

Find the rates of change of total revenue, cost, and profit with respect to time. Assume that \(R(x)\) and \(C(x)\) are in dollars. \(R(x)=2 x\) \(C(x)=0.01 x^{2}+0.6 x+30\) when \(x=20\) and \(d x / d t=8\) units per day

A sporting goods store sells 100 pool tables per year. It costs 20 dollars to store one pool table for a year. To reorder, there is a fixed cost of 40 dollars per shipment plus 16 dollars for each pool table. How many times per year should the store order pool tables, and in what lot size, in order to minimize inventory costs?