Given the production function per hour Q(x, y) = −2x² − 4y² + 40 + 40y, where x is a worker receiving $1 per hour and y is a worker receiving $2 per hour. The budget constraint is $410. What is the value of |Ā?
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- 1. Inputs K, L, R and M cost £10, £6, £15 and £3 respectively per unit. What is the cheapest way of producing an output of 900 units if a firm operates with the production function Q = 20K0.4L0.3R0.2M0.25? 2. Make up your own constrained optimization problem for an objective function with three variables and solve it. 3. A firm faces the production function Q = 50K0.5L0.2R0.25 and is required to produce an output level of 1,913 units. What is the cheapest way of doing this if the per-unit costs of inputs K, L and R are £80, £24 and £45 respectively?A firm has a production function of q=2(LK), where the L represents hours of labor, K represents hours of machine usage and q represents the hourly production volume. Currently the price of labor is $20 per hour and the price of capital is $40 per hour. a. When the production level is at 40,000 units, use the LaGrange process to determine how much they should spend on labor and capital. b. If the purchasing agent requests an additional unit (40,001st unit), what is the minimum price you should charge on that specific unit? (Note: determine this without re-solving the Lagrange problem itself.)The inventory cost C of stocking a lot of size x is given by the function C(x)=8.1x+5,000x−1+675. What lot size would minimize costs? Round to the nearest whole number.
- The cost (C) of a apples in dollars can be represented by the function C(a)=0.27a, and the cost (P) in dollars of b bananas can be represented by the function P(b)=kb, where k is a constant. If C(10)+P(8)=$5.34, what is k ?If the production function of a firm is given by Q=K2L3 and the input prices are r = Birr 8 per unit and w = Birr 2 per unit, Find the levels of labor and capital that maximize the level of output for a total outlay of Birr 240.If the production function of a firm is given by Q=K2L3 and the input prices are r=Birr 8 per unit and w= Birr 2 per unit, find the levels of labor and capital that maximize the level of output bfor a total outlay of birr 240.
- A convenience store manager earns a base salary plus a small bonus of $60 for each of ten different possible monthly milestones he meets. If the manager meets a milestone, the full bonus is paid. However, if the manager falls even one penny short, none of that bonus is paid. Suppose each of the ten milestones requires 40 hours of effort to meet, and that the manager has 160 hours of effort to allocate to work each month. In order to maximize the total monthly bonus, the manager should allocate hours toward meeting each of milestones and hours toward meeting each of the remaining sales milestones.The technical rate of substitution between factors x2 and x1 is −4. If you desire to produce the same amount of output but cut your use of x1 by 3 units, how many more units of x2 will you need?Determine the combination of input factors K, L that minimizes the cost of producing Q.
- A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplierThe total cost (in dollars) to produce qq units of a good is given by the function:C(q)=7.6q+44000C(q)=7.6q+44000A. What is the total cost to produce q=4800q=4800 units?Total cost = $ B. What is the cost of the 48014801st item?Cost of the 48014801st item = $For the typical Cobb-douglas function, q=AKaLb whereas APL / APK = 1 , find out the marginal rate of technical substitution.
