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- For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1 X1 3-2 x2 Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3 Consider the following function: f(x1, x2) = 2x1 - x-x+3. - For your visual convenience, a portion of the function is depicted in Figure 2. (a) Compute the gradient vector of f. (b) Compute the Hessian matrix of f. (c) Determine all points that yield stationary values of f. (d) Use the second-order conditions to determine whether each of the stationary val- ues of f is a maximum, a minimum, or neither.22.5 Recall that Touchie McFeelie's production function for comic books is .1J1/213/4. Suppose that Touchie can vary both jokes and cartoonists' labor. If old jokes cost $2 each and cartoonists' labor costs $18 per hour, then the cheapest way to produce comics books requires using jokes and labor in the ratio J/L= (a) 9. (b) 12. (c) 3. (d) 2/3. (e) X+ PC X4.0 Show Transcribed Text 000 please explain this question and the correct answer is 6. Thanks.
- Differentiate the function. g(x) = (x⁹ - 8x)-2 g'(x) = Differentiate the function. 5 f'(s) = f(s) = (2s7 + 1)4 Differentiate the function. 1 g(x) = (2x+5x+1) 3/4 g'(x) = Differentiate the function. dy y = √√√3x² + 6x + 2 dxSuppose you have t = 5 hours in total to spend on some projects to make some money. The table below shows how many dollars you can make (Total Revenue) in each of the three projects I, II, III if you spend the corresponding number of hours on that project: How would you allocate your time across the projects?What is the maximum total money you could make?1. Assume you must choose between two mutually exclusive alternatives: A or B. The explicit benefit you receive from alternative A, bª, is equal to $100. And, the explicit cost of choosing alternative A, c*, is $80. Also, the explicit benefit to choosing alternative B, b", is $120. What is the accounting return for choosing alternative A, r^? Given r and b", what is the explicit cost that you are willingness to pay (WTP) for alternative B, WTP"? Please include the formulas from class in your answer. How would WTPB change ifr^ increased by $5? Explain. your Using the original set of values for explicit costs and benefits, what would be your economic return to choosing alternative How does this relate to the concept of consumer surplus? if the price that you were charged was $95? Please interpret.
- None***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…Question 5 A manufacturing company produces the quantity q of a product that depends on I units of labour and a capital amount K as given by the equation 3 1 q = 6 (L) ³² (K) ² Labour costs are $10 per labour unit and capital costs are $20 per unit of capital and the total cost budget is $3,000. (a) Find the optimal solution using Lagrange Multipliers. G (b) Demonstrate the following economic principle for the optimal solution found in (a) that The marginal productivity of labour / The marginal productivity of capital = aq = Cost per unit of labour / Cost per unit of capital aq ☆ ƏL Challenge Level (c) Recompute the optimal values for L and K when the budget is increased by $1 and check that this allows for the production of an extra λ units where is the Lagrangian multiplier.
- 3. Suppose that the feasible region of a cost minimization linear programming problem has three corners points of (5,8), (10,5), and (4,10). If the objective function is given as: Minimize Z = 2X + Y Which of the following represents an iso-cost line? Select one: a. X + 2Y = 10 b. X – Y = 10 c. 2X – Y = 10 d. 2X + Y = 10 e. none of the other options.The time path of resources is described by X(t) = X(0)e*". If you graphed In X(t) on the y-axis, and had time (t) on the x-axis, then what would be the intercept of the line you drew? In X(0) There isn't enough information to tell gx