Find the number of units x that produces the minimum average cost per unit E in the given equation. C = 0.001;:3 + 3x + 128 Consider the following. C=x3 6x1+ 1.8x Use the cost function to find the production level at which the average cost is a minimum. For this production level, Show that the marginal cost and average cost are equal. Use a graphing utility to graph the average cost function and verify your results. marginal cost 5 E Consider the following. P = 0.153 + 652 + 400 Find the amount 5 of advertising (in thousands of dollars} that maximizes the profit P [in thousands of dollars). Find the point of diminishing returns. we ) A real estate office handles a 80-unit apartment complex. When the rent is $580 per month, all units are occupied. For each $45 increase in rent, however, an average of one unit becomes vacant. Each occupied unit requires an average of $70 per month for service and repairs. What rent should be charged to obtain a maximum profit? $ XUse a graphing utility or spreadsheet software program to complete the table. Then use tlie result to estimate the limit of f(x) as x approaches infinity. (Round your answers to six decimal places.) f(x) = \"X x2+3 x 100 101 102 103 104 105 106 f(x)| ll ll || ll ll ll x2m The cost C (in dollars) of supplying recycling bins to p% of the population in a rural township is modeled by 13300;; 0 4 C: 100p p 100'. \"m 13,000p = p>100_ 100 p Interpret the limit in the context of the problem. Use a graphing utility to verify your result. as the percent of the rural population being supplied with recycling bins approaches 100%, the cost