MC = 10q, ATC = 10/q+ 5q, AVC = 5 q, AFC = 10/q I would like to know how to plot them(in graph) in the figure as shown (dont understand how it is ploted) ว ง 9 = √KE C 10K+5E K=1 C(q)=10+5q2 Market price (P) = 30 P = MC 30 = 10q q=3 Profit per unit = π R TC = q = P - ATC q q π = (PATC)q p=30 Cost Curves for C(q)=10+5q2 MC Profit ATC AVC AFC
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- 1. ThedemandfunctionforagoodisgivenbytheequationP=a−bQwhilethetotalcost function is TC = dQ2 + eQ + f, where a, b, d, e and f are positive constants. (a) Derive the equation for profit.(b) Derive an expression for the value of Q for which profit is maximised.Pixie Arts and Graphics, a medium scale printing press business has determined the equation that describes the relationship of the price and demand of one of its products as Price=150 - 0.01•D (D as Demand per unit) for an annual printing of this product. The fixed costs annually = P50,000 and the variable cost = P40 per unit. Requirement: a. What is the maximum profit that can be earned? b. What is the unit price at this point of optimal demand if demand is not to be anticipated to exceed more than 6,000 units annually? Hint: Profit (loss) = total revenue – total costs = (aD – bD²) – (Cf + CyD)??????? ?(a) Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q.(i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J′s profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing whenhe produces 5 hundred, 750ml bottles of dishwashing liquid.(iv) How many 750ml bottles of dishwashing liquid should Teddy J produceper month if he wishes to maximize his profits.(b) A firm has an average cost functionA(q) =125q+q216 − 4.where q is the firm′s output.(i) Determine the level of output for average costs are minimum.(ii) Hence determine the range of values for which average costs are decreasing.(iii) What part of the decreasing range is practically feasible?(iv) Write an equation for the total cost function.(v) Hence calculate the level of output for which total costs are minimum.
- Sampson Ltd produces two products that can be produced on either of two machines. Each month, only 5o0 hours of time are available on each machine. The time required to produce each item by hour and machine is: Machine Machine Product 1 Product 2 3 4 Month Month 1 Month 2 Month 1 Demand Demand Price Price Product 1 100 160 $45 $65 $10 Product 2 120 110 $35 The demand and price point for each product that customers are willing to pay are above. The company goal is to maximize revenue from sales from the next two months. Based on the provided information, how many constraints does this problem have excluding the non-negativity constraints?PakPerfect Inc. estimates equation of its total costs of production as TC = 500 + 10Q + 5Q2 and market demand for its product as Qd = 105 – (1/2) P, where Q is quantity in units and P is price in Pak$. (i) Write the equations of the firm’s costs, as a function of Q (ii) Average Total Cost ATC (iii) Average Variable Cost AVC (iv) Average Fixed Cost AFC a. Given above costs can you determine what will be the firm’s production in Stage 1? What is the breakeven price and breakeven quantity for this firm? b. What is the shutdown price and quantity for this firm? c. Draw the firm’s costs in a graph as per your determination in (a). Label the breakeven and shutdown price and quantity using information in (b) and (c) above. d. Given the market price of Pak$ 50 (i) how many units should the firm produce? (ii) how many firms are competing in this market in short-run? (iii) How many firms will be in the industry in the long-run? e. How do you interpret the profit or loss condition of PakPerfect?…Given Cost and Price (demand) functions C(q) = 110q + 45000 and p(q) = - 2.8q + 800, what profit can be earned if the price is set to be $550 per item? U The profit is $ 1,?9 (Round to the nearest cent.) A company produces a special new type of TV. The company has fixed costs of $499,000, and it costs STT00 to produce each TV. The company projects that if it charges a price of $2300 for the TV, it will be able to sell 850 TVs. If the company wants to sell 900 TVs, however, it must lower the price to $2000. Assumo a linear demand. What is the marginal profit if 200 TVs are produced It is $ 0 per item. (Round answer to nearest dollar.)
- The Talbot Company uses electrical assemblies to produce an array of small appliances. One of its high cost / high volume assemblies, the XO-01, has an estimated annual demand of 8,000 units. Talbot estimates the cost to place an order is $50, and the holding cost for each assembly is $20 per year. The company operates 250 days per year.A toy manufacturer makes miniature trucks. The pricep(in dollar) and the demandx(numberof miniature trucks) are related by the equation 6000−600p=x. The total cost for the sametoy manufacturer to producexminiature trucks can be modeled byC(x) = 8x+ 450.(a) (10 points) Express the pricepin terms of the demandx. Find the revenueR(x) if themanufacturer sellsxminiature trucks in a month and find the domain of this function.(b) (10 points) Graph the cost and revenue functions on the same coordinate system for 0≤x≤6000.(c) (10 points) What is the minimum number of trucks the toy manufacturer must sell tobreak even?(d) (10 points) FindP′(300) and interpret the result.(e) (10 points) What is the exact profit from the sale of the 301stminiature truck?Given Question #1 Cost function C= 3000+6Q Q = 4400 - 200Q Q= 1600 P = 14 Profit= 22400-12600 = 9800 Question #2 Q=$480 - Laredo Q=$1120 - SA Question #3 Ed=−1.25 - Laredo Ed=−0.55 - SA 0.5<0.8− markup index it is charging less. - Laredo 0.64<-1/-0.55--markup index it is charging less. - SA Please answer question number #4 A-C
- Given Question #1 Cost function C= 3000+6Q Q = 4400 - 200Q Q= 1600 P = 14 Profit= 22400-12600 = 9800 Question #2 Q=$480 - Laredo Q=$1120 - SA Question #3 Ed=−1.25 - Laredo Ed=−0.55 - SA 0.5<0.8− markup index it is charging less. - Laredo 0.64<-1/-0.55--markup index it is charging less. - SA Please answer question number #4 (A-C) For Laredo only2. A company produces and sells a consumer product and is able to control the demand for the product by varying the selling price. The approximate relationship between price and demand is 2,700 5,000 p = $38 + D for D >1 D2 where p is the price per unit in dollars and D is the demand per month. The company is seeking to maximize its profit. The fixed cost is $1,000 per month and the variable cost (c,) is $40 per unit. a. What is the number of units that should be produced and sold each month to maximize profit? b. Show that your answer to Part (a) maximizes profit.As per given information, the table is completed:- (In $) Quantity Price Total Marginal Total Cost Marginal Revenue Revenue Cost 34 20 20 1 32 32 32 36 16 2 30 60 28 46 10 28 84 24 50 4 4 26 104 20 54 4 24 120 16 56 2 22 132 12 64 7 20 140 80 16 8 18 144 4 100 20 16 144 128 28 14 140 -4 160 32 (d) Generally, what are the relative values of price, ATC, and AVC when a monopolist experiences: a profit? a loss but continues to produce? a loss but ceases production? 10