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- Find two nonnegative number x and y for which x+3y=30, such that x2y is maximized.If the utility function of an individual takes the form U=U(x1,x2 )=(x1+2 )2(x2+3)3 Where U is total utility, and x1 and x2 are the quantities of two commodities consumed:i. Find the marginal utility function of each of the two commodities.ii. Find the value of the marginal utility of the first commodity when 3 units of eachcommodity are consumed.Suppose the Sunglasses Hut Company has a profit function given by P(q)=−0.03q2+4q−46P(q)=-0.03q2+4q-46, where qq is the number of thousands of pairs of sunglasses sold and produced, and P(q)P(q) is the total profit, in thousands of dollars, from selling and producing qq pairs of sunglasses.A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: MP(q)=MP(q)= B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected.
- 11) Find each of the two areas bounded by the curves y = x3-4x and y = x² + 2x. Points of intersection: (0, 0), (3, 15) and (-2, 0) (-2, 0) (-1.15, 3.08) A da (-1,-1) (3, 15) (1.15,-3.08)1. A certain manufacturer produces door handles and has a profit function P(x) = 5x – 0.05x? – 450 when x door handles are sold. a) What is the company's profit if 150 handles are sold? Does the result make sense? b) What is the company's profit of the sale of the 151th unit? c) What is the company's marginal profit function?Suppose the Sunglasses Hut Company has a profit function given by P(q) = -0.02q² +3q - 36, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing a pairs of sunglasses. A) Find a simplified expression for the marginal profit function. (Be sure to use the proper variable in your answer.) Answer: P'(q) B) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: thousand pairs of sunglasses need to be sold. C) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: thousand dollars of maximum profits can be expected.
- A linear revenue function is R=40x A)what is the slope? B)What is the marginal revenue? C)What is the revenue received from selling one more item if 50 are currently being sold?5. Find the area of a parallelogram bounded by the y-axis, the line x = 3, the line f (x) = 1 + 2x, and the line parallel to f (x) passing through (2, 7).17. The cobb douglas production function for a product is N(x,y)=10x8y2 Where x is the number of units of labor and y is the number of units of capital required to produce N units of a product. a.) If the company is now using 40 units of labor and 50 units of capital, find the marginal productivity of labor and the marginal productivity of capital. c.) For the greatest increase in the company's productivity, should the company encourage increased use of labor or increased use of capital? please show all work. Thank you!!
- Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A's utility function is given by: UA(X. Y) = X*Y3 And consumer B's utility function is given by UB(X,Y) = X*Y. Therefore, consumer A's marginal utilities for each good are given by: MUy = Y3 MUy=3X*Y2 Also, consumer B's marginal utilities for each good are given by: MUx= Y MUy = X Initial Endowments are given by Person A has 40 units of good X and 20 units of good Y. Person B has 30 units of good X and 20 units of good Y. Suppose Py = 1, a) What is the value of Py that will result in a competitive equilibrium? (Ans: Py=1/3, but I don't know why) b) How much of each good will each consumer demand in equilibrium2.(25) let h(y)The area bounded by the curve y = 4x and the lines a = 6 ,x = 12 and x - axis is 144 square units O 360 square units 5184 square units O 216 square units
