1. The cost function for a commodity is given by C(x)- 200+12x+0.1x² (S) and the demand functi is p-300-0.02x ($/unit) where x - quantity (demanded and produced). (a) What is the profit function for this commodity? (b) Find the marginal profit function. (c) What is the marginal profit when x-10?
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- 1. Assume the cost of making 30 belts is $800, the cost of making 35 belts is $910, and the cost equation is linear. The belts are sold for $27 each. Find the marginal cost of production. (b) Find a linear equation in slope-intercept form that will represent the total cost of making x belts. (c) What is the fixed cost? (a) (d) Find a profit equation in slope-intercept form that will represent the profit if x belts are made and sold. (e) Find the break-even point.Quantity Fixed Costs Variable Costs Total Cost Marginal Cost 10 200 50 250 *********** 20 200 100 300 5 30 200 300 500 20 40 200 800 1000 X (A) If the equilibrium price is $20, find the profit-maximizing quantity. (B) How much profit will the firm earn? (C) Find the marginal cost as X.The demand for q units of a product depends on the price p (in dollars) according to 512 P q= - 1, for p > 0. Find and explain the meaning of the instantaneous rate of change of demand with respect to price when the price is as follows. (a) $16 (b) $64 Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units. If price decreases by $1, the demand will drop by the absolute value of this number of units. If price increases by the absolute value of this amount, the demand will drop by 1 unit. If price increases by $1, the demand will drop by the absolute value of this number of units. Interpret the instantaneous rate of change. O If price decreases by the absolute value of this amount, the demand will drop by 1 unit. O If price increases by $1, the demand will increase by the absolute value of this number of units.…
- 1. (a) A company expects fixed cost of $55,000. Margin is to be 46 percent of the retail. Variable cost in addition to costs of goods is estimated at $0.06 per dollars of sale. Find the profit function using s for sales volume. (b) Square Hospital Limited charges every COVID patient a fixed amount for using their ICU facilities. What would be the graphical nature of the demand function of ICU in this case ? (c) Write down the general form of the Augmented matrix of a system of Linear Equation which consists of 5 equations and 4 unknowns. (0.5 0.5 (d) Calculate the steady state vector for the given transition matrix: (e) Assuming the nonnegativity constraints for each variables, calculate the total number of corner points for the following system of inequalities: 2x + 5y + 4z 2 29 3r + 2y + z 2 23 10r + 8y +5z > 62You’ve been given a firm’s production and cost functions:p = 132 −2qMC = 12 + 4q(a) Assume this firm is in a perfectly competitive market. Calculate the equilibrium price andquantity.(b) What is the firm’s profit here?(c) Assume this firm is in a monopoly market. Calculate the equilibrium price and quantity.(d) What is the firm’s profit here?(e) Give an example of a perfectly competitive agricultural market, and give an example of amonopoly agricultural market.2. The relationship between price and demand per month for a consumer product is p = 3500 -1.1D5 where p is the price per unit in dollars and D is the demand in units. The fixed cost is $300 per month and the variable cost is $4.00 per unit. What is the optimal number of units that should be produced and sold per month? a. b. What is the maximum profit per month?
- Suppose the supply for a certain textbook is given by p=-q² and demand is given by p= 4 where p is the price and q is the quantity. (a) How many books are demanded at a price of $15? (b) How many books are supplied at a price of $15? (c) Graph the supply and demand functions on the same axes. +20,C(x) = 0.01x-0.3x + 10x gives the cost, in thousands of dollars, to produce x thousand items. (a) Find a formula for the marginal cost. (b) Find C'(0). Give units. (c) Graph the marginal cost function. Use your graph to find the minimum marginal cost, the production level for which the marginal cost is the smallest. (d) For what value of x does the marginal cost return to C'(0)? (a) Find a formula for the marginal cost. c'(x) =D (b) Find C'(0). Give units. c'(0) = (c) Use the derivative of the marginal cost function to find the minimum marginal cost, the production level for which the marginal cost is the smallest. The minimum marginal cost of additional dollars per item produced occurs when thousand items are produced. d) Recall your answer to part b. For what value of x does the marginal cost return to C'(0)? Marginal cost returns to this value of C (x) when x = items are produced.) A company manufacturing laundry sinks has fixed costs of $100 per day but has totalcosts of $2,500 per day when producing 15 sinks. The company has a daily demand functionof q = 360 − p, where q is the number if laundry sinks demanded and p is te price ofa laundry sink. Find a function for the average cost of this company. (c) If production increases continuously, what is likely to be the average cost per sink? (d) How many laundry sinks will the company need to produce in order to maximise it′s profits? (e) What is the maximum profit?
- A firm in a perfectly competitive industry has fixed costs of FC = 15, marginal costs of MC = 5 + 14q, and average variable costs of AVC = 5 + 7q. (a) What are the firm’s variable costs (VC)? (b) What is the firm’s total cost function? (c) If the price is $75, how much does the firm supply? (d) Does the firm continue to supply this quantity in the short-run? (e) Suppose there exists a standard market demand function from consumers (downward slopping). Please provide a logical discussion about how the market achieves short-run equilibrium.12 st L8 Get & Transform Data 4 6 7 1 2 Available Product 3 8 9 10 11 12 13 A 14 15 16 17 18 19 20 All :X ✓ fx B Pounds made Workbook Links Queries & Connections 3000 Flour (ounce) 1500 Egg (piece) 4500 Labor (man-hour) Unit Price Variable Cost Demand UCM Adiucted C 3.2 1.5 6 D $12.50 $6.50 960 $6.00 2.6 1.5 5 Data Types $11.00 $5.70 928 $5.30 E 1.5 1 4 <1 $9.00 $3.60 1041 $5.40 F 0 0 0 0 Banana Muffin Choc Muffin Banana Cookies Choc Cookies Milk Bread White Bread 0.7 0.3 0.5 0 2.5 1.5 $6.00 $3.00 $2.20 $1.20 1084 1055 $3.80 $1.80 AV 0 0.8 1 3 G $7.00 $2.80 977 $4.20 Sort & Filter H Advanced 0What is the marginal cost associated with producing three units of the contral variable, O (identify point E in the tablej? 36 Total Total Costs Benefits Benefit Net Marginal Marginal Narginal Net Bеnefit Control variable Benefits Cost MB(0) MC (Q) MND (0) Sepped B(Q) C(0) 900 100 800 900 100 800 2 1,700 300 800 200 600 2,400 600 1,800 700 E 400 4 1,000 2,000 600 400 200 3,500 1,500 2,000 500 500 600 1,800 1,400 3,900 2,100 D -200 4,200 4,400 2,800 300 700 -400 200 100 800 800 -600 4,500 4,500 900 -800 10 4,500 5,500 -1,000 1,000 -1,000 Mutiple Choice 50 100 200 300