[A] Production Econ-Exercise 3- 2022.pdf - Adobe Acrobat Reader DC (64-bit) X File Edit View Sign Window Help Home Tools Production Econ-Ex... x ? A Sign In T 1 /2 105% X CACICISE S Lov mains] 7707 /co/ 17 A 1. Consider the production function of maize output as follows: Y= 100 + 400x - 2x2, where Y = maize output (kg) and X = fertilizer application (kg), calculate the LO a) Level of input that will maximize maize output. [4] b) Optimum quantity of maize that could be produced. [6] 2. A farmer sells cabbages for N$10 per head. The farmer's variable costs are N$2.50 per head and total cost of 100 heads is N$1450. a) How many cabbages must the manufacturer produce each month to break even? b) How man cabbages should be produced to make profit Co 3. Total cost of producing carrots is C(x) = 3600+100x+2x2 and the total revenue function R(x) =500x-2x2 a) Find the number of kg that maximizes profit b) Find maximum profit 4. What is the mathematical criterion for a cost-minimization choice of labour and capital? 5. Suppose a production function is given by Q= KO.410-s, subject to 3k + 4L = 108, find the optimal condition of capital (K) and labour (L). [10] 4 6. The quantity demanded each month is related to the unit price by the equation: P = 40 0.02x2+3 , find the marginal revenue (MR) function 'R. [4] 7. A farmer owns a 100 hectares farm and plans to plant at most three crops. The seed for wheat, maize, and sorghum costs $40, $20, and $30 per hectares, respectively. A maximum of $3200 can be spent on seed. Wheat, maize, and sorghum require 1,2, and 1 workdays per hectares, respectively, and there are maximum of 160 workdays available. The farmer can make a profit of $100 per hectares on wheat, $300 per hectares on maize, and $200 per hectares on sorghum. Prepare the elevant linear programming model to determine how many ha of each crop should be planted to maximize profit. [14] 8. Suppose that the demand equation for a company is p = 100 - .01x and the cost function is C(x) = 50x + 10,000. Find the, a) value of x that maximizes the profit; b) determine the corresponding price and c) total profit for this level of production. 9. Briefly explain the following concepts; Type here to search A DOOORE Oh 90C ~ 9 1 7 () ENG 6:42 PM 9/27/2022