(a) Using Lagrange multipliers calculate the maximum possible output Q when the total input cost is $200. (b) Measuring labour (L) on X-axis and capital (K) on Y-axis, show the optimal level of Lar K in a diagram.
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- Maximize the function fx,y=7x+5y in the region determined by the constraints of Problem 34.A firm has 2 plants with different functions: - Plant 1: MC = 30 + Q - Plant 2: MC = 20 + 2Q How to allocation output between the 2 plants to minimize total cost of producing 50 units of output? What is the minimum total cost?the quantity, q, of a product manufactures depends on the number of workers.W , and the amount of capital invested, K, and is represented by the Cobb-Douglasfunctionq = 64W^3/4 K^1/4 .Suppose further that labor costs $18 per worker and capital costs $28 per unit, and thebudget is $4600. Let λ be the Lagrange multiplier. Does increasing the budget by $1 allow theproduction of λ extra units of the product? Explain why as shown in the image below..
- A firm producing two goods, x and y, has the cost function given byC( x , y )=(1/100)x2−10x+(1/300)y3−9y+20,600a. Find the cost minimizing level of output for each of the two goods.b. Check to be sure cost is minimized. c. Find the corresponding cost.Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is x = 85 − p1 thousand units and the demand for brand 2 is y = 95 − p2 thousand units, where p1 and p2 are prices in dollars. If the joint cost function is C = xy, in thousands of dollars, how many of each brand should be produced to maximize profit?A firm has two plants, X and Y. Suppose that the cost of producing x units at plant X is x^2 + 12000 dollars and the cost of producing y units of the same product at plant Y is given by 3y^2 + 800 dollars. If the firm has an order for 1200 units, how many should it produce at each plant to fill this order and minimize the cost of production (use Lagrange multiplier)? Answer in complete solutions please. Thank you.
- A firm has two plants that produce identical output. The costs functions are C1=10q-4q^2+q^3 MC1 = 10 - 8q + 3q^2 and C2 = 10q - 2q^2 + q^3 MC2 = 10 - 4q + 3q^2 a. At what output levels does the average cost curve of each plant reach its minimum? b. If the firm wants to produce four units of output, how much should it produce in each plant?Suppose that a company has received an order for 200 units of its product and wishes to distribute its production between two of its plants, Plant 1 and Plant 2. Let x and y be the outputs of plants 1 and 2, respectively, and suppose that the function of total cost is given by c = f(x,y) = 2x2 + xy + y2 + 200 How should production be distributed to minimize costs? What would you do if now instead of 1 restriction, you had 2 restrictions?1.A box with a square base and open top should have a volume of 50cm3. Using Lagrange multipliers find the dimensions of the box that minimize the amount of material to be used.
- A function, z = ax + by, is to be optimized subject to the constraint, x2 + y2=1 where a and b are positive constants. Use Lagrange multipliers to show that this problem has only one solution in the positive quadrant (i.e. in the region x > 0, y > 0) and that the optimal value of z is √a2 +b2.3. If you want to design a pop can to hold 350 cm3 of pop using the least amount of metal to make the can, what would you use for f and g in the Lagrange Multiplier Method?Can I get some assistance with this coordinatization problem?