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Q.2 Determine the values of K and L which minimise the cost function C = 3K + 5L subject to the production constraint, 250 = 10K0.5L0.5.
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- 1/3 1/3 Farmer Joe's production function is f(x1, x2) = ", where xị is the number of pounds of lemons he uses and x2 is the number of hours he spends 1/21/2 2wi"wy3/2, where y is the squeezing them. His cost function is c(w1. w2, y) = number of units of lemonade produced. (a) If lemons cost $1 per pound, the wage rate is $1 per hour, and the price of lemonade is p, what is his marginal cost function?You start creating personalized iPhone cases. Suppose the quantity of cases demanded each month is related to the price by the equation p- 1600 - 20g where p is the price per case in dollars and q is the mumber of cases. Your total cost to manufacture q cases is given by 10g? + 30 180 – 2g C(9) = (a) Find the average cost function (simplify where possible). (b) Find the total profit as a function of q. (c) Find your marginal profit at a demand level of 60 cases per month and write a sentence interpreting what your answer means in terms of your busi- ness. Include units.Here is the production cost function, in $ of producing q units of a product: 2200 C(q) = 300 +0.8q2 + %3D and the demand function of the product is: p(x) = 200 - 0.05q a. Determine the marginal cost, marginal revenue and marginal profit when q=50 and q=150? b. Interpret the results of the calculation in part (a) if it is related to cost, revenue and profit?
- A firm's average cost (AC) per unit of output depends on the number of hours of skilled labor (S) and the number of hours of unskilled labour (U) employed in the production process. The firm's AC function is defined below. Determine the quantities of the two inputs that will result in production at the lowest possible average cost and determine the associated minimum average cost. AC = 3S2 + 2U2 - 2SU - 2S - 6U + 20firm's average cost (AC) per unit of output depends on the number of hours of skilled labor (S) and the number of hours of unskilled labor (U) employed in the production process. The firm's AC function is defined below. Determine the quantities of the two inputs that will result in production at the lowest possible average cost and determine the associated minimum average cost. AC-3S2+2U2-2SU-2S-6U+ 20Suppose that the monthly cost, in dollars, of producing x chairs is C(x)=0.005x³ +0.07x² +19x + 700, and currently 35 chairs are produced monthly. a) What is the current monthly cost? b)What is the marginal cost when x = 35? c) Use the result from part (b) to estimate the monthly cost of increasing production to 37 chairs per month. d)What would be the actual additional monthly cost of increasing production to 37 chairs monthly? a) The current monthly cost is $ (Round to the nearest cent as needed) b) The marginal cost when x = 35 is $ per item. (Round to the nearest cent as needed.) c) Use the result from part (b) to estimate the monthly cost of increasing production to 37 chairs per month. The monthly cost in increasing production to 37 chairs monthly is $ (Round to the nearest cent as needed) d) The actual additional monthly cost of increasing production to 37 chairs monthly is $ (Round to the nearest cent as needed.)
- For a cost function C = 100 - 100 - Q2 the average variable cost of producing 20 units of outout isGive the formulas for and plot AFC, MC, AVC, and AC if the cost function is a C = 10+10q (MC = 10) b C = 10 + q2 (MC=2q). c C = 10 + 10q - 4q2 + q3 (MC = 10 - 8q + 3q2). ATC AVC AFCConsider the following function: Ĉ = 0.03q + 6 + 200/q - determine the approximate cost to increase production from 200 units to 201 units - determine the function of marginal cost
