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2.In Andrew’s Furniture Shop, he assembles both bookcases and TV stands. Each type of furniture takes him about the same ...

s him about the same time to assemble. He figures he has time to make at most 18 pieces of furniture by this Saturday. The materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00. He has $600.00 to spend on materials. Andrew makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand. Find how many of each piece of furniture Andrew should make so that he maximizes his profit. Using the information in the problem, write the constraints. Let x represent number of bookcases, and y represent number of TV stands.
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3. The marketing research department for the company that manufactures and sells “notebook” computers established the following price – demand function: p(x) ...

ters established the following price – demand function: p(x) = 10 – 0,001x, where p(x) is the wholesale price in dollars at which x thousand computers can be sold. Total cost (in dollars) of producing x items is given by C(x) = 7000 + 2x. A) Find the revenue function and state its domain. B) Find the marginal revenue function. Find R´(4000) and R´(6000). Interpret the results. C) Evaluate the approximate revenue and exact revenue of producing 101-th notebook. D) Find the profit function E) Find the marginal profit function. F) Evaluate the approximate profit and exact profit of producing 101-th notebook. G) Find P´(5000) and P´(7000). Interpret the results.
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4.(d) The random variable X takes only the values 3, 5, 8 and 10 according to the following probability distribution: x 3 ...

ty distribution: x 3 5 8 10 pX(x) k k k 2k i. Determine the constant k and hence write down the probability distribution of X. ii. Find E(X), the expected value of X. iii. Find Var(X), the variance of X.
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6.I am trying to figure out the optimal radius that will give the lowest surface area of a cylinder. I ...

have done the calculus which reveals that the surface area is at a minimum when height is double the radius. I am now trying to find an equation for the relationship between the amount of wasted surface area as a percentage of the minimum surface area and the ratio between height and radius. If I were to plot it on a graph, the y axis would be the percentage of excess materials needed as a percentage of the minimum possible surface area, and the x axis would be height divided by radius. Since the surface area is minimized when height=2(radius), I know that when x=2, y=0. The website explains what I am trying to do quite well and shows the graph below. I am trying to find the equation for this graph, but am unsure how to go about it.
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

mathematicsalgebra Physics