Assume that F(X,, X,) = X,1/3 X,1/3 W, = 1, w2 = 2, p = 3 Please solve the above profit maximization problem (unconstrained optimization) for the optimal quantities X,* and X,* showing step-by-step solution.
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A: 200-4Q = Q^2 + 6Q +125 Q^2 + 10Q - 75 = 0 (Q-5) (Q+15) = 0 Q* = 5 TR = 200*5 -2*5^2 = 1000-50 = 950…
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- Suppose the joint cost function of a firm producing two products X and Y is given by C = 250X2 + 120Y2. Assuming that output of the two products is restricted at 4144. Using Lagrangian multiplier technique find the amounts of X and Y that will minimize cost and compute this cost. Also examine the cost implications of changing this optimal combination so as to produce equal amounts of both products.Given: TC = 100 + 60Q – 12Q2 + Q3. Solve the level of output at which the AVC curve is in minimum. With proper solution.PakPerfect Inc. estimates equation of its total costs of production as TC = 500 + 10Q + 5Q2 and market demand for its product as Qd = 105 – (1/2) P, where Q is quantity in units and P is price in Pak$. Write the equations of the firm’s costs, as a function of Q: Average Total Cost ATC Average Variable Cost AVC Average Fixed Cost AFC Given above costs can you determine what will be the firm’s production in Stage 1? What is the breakeven price and breakeven quantity for this firm? What is the shutdown price and quantity for this firm? Draw the firm’s costs in a graph as per your determination in (a). Label the breakeven and shutdown price and quantity using information in (b) and (c) above. Given the market price of Pak$ 50 how many units should the firm produce? how many firms are competing in this market in short-run? How many firms will be in the industry in the long-run? How do you interpret the profit or loss condition of PakPerfect? Use a two-panel graph of the Market and…
- A company has determined that the price and the monthly demand of one of its products are related by the equation D = (400 - P)1/2 , where p is the price per unit in dollars and D is the monthly demand. If the associated fixed costs are $1,125/month, and the variable costs are $100/unit, what is the optimal number of units that should be produced and sold each month to maximize the profit?A firm’s marginal cost and revenue functions are given byMC = 12q2 + 16q + 20MR = 100 –2q a. Rewrite the above equations as first order differential equations.b. If the firm’s total costs are 3360 when output q = 10 and its total revenue is 0 when q = 0, Solve the ODEs to find the firm’s total cost and total revenue functions. c. Hence derive the firm’s fixed costs.Given that the marginal cost of a ‘backstop’ (e.g. solar energy) is MCb per unit of an exhaustible resource, prove that the cost of the ‘backstop’ sets an upper limit on oil price and also determines the initial price of oil. (Hint:Utilize the expression pt = MC + (p0 − MC)(1 + r)t and consider T as theswitch date.)
- (You will need to use a spreadsheet to tackle these questions.) 1. How much of q can be produced for £60,000 if the total cost function is TC = 86 + 152q − 12q2 + 0.6q3? 2. What output can be produced for £150,000 if TC = 130 + 62q − 3.5q2 + 0.15q3? 3. Solve for x when 0 = −1,340 + 14x + 2x2 − 1.5x3 + 0.2x4 + 0.005x5 − 0.0002x6You are managing sports apparel sales. The way contracts are writlen, you purchase the rights to buy a fixed block of copyrighted materials for a negotiated price for a given yoar. You then sell these materials through your channels and try to make the moat possible. Apparel sales are automated through online channels so the additional cost of selling a given unit is negligible. In other words, the cost structure is relatively fixed no matter how many units you sell. What is an aporopriate optimization target for this type of cost structure and what will elasticity equal if you optimize prices well?an American multinational that sells consumer electronic products, has manufacturing facilities in three countries: Brazil, Thailand, and Canada. The average hourly wage rate, output per worker, and annual overhead cost for each location are as follows: Given the above figures, is Storm currently allocating its production resources optimally? If not, what should it do? Justify your answer. Now, suppose that Storm is planning to consolidate all its manufacturing into one facility. Where should it locate? Justify your answer.