The price and cost functions in ringgit of a product are given as p= 600-x and C(x)= 200+6x+2x. If company is producing 95 units of the product, which output level will give more profit from 95 units of production. L 105 II. 100 III. 102 IV. 98
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- Dollars per unit $60- 56 52 48E MC 44 40 - MR =D 36F ATC 28 AVC 24 20 16 12 8- 100 150 200 250 Referring to the graph above, the profit-maximizing quantity is 250 200 100 150 62 8 ↑ O6 2 0Sampson 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 $35 The demand and price point for each product that customers are willing to pay are above. The company goal is to maximize revenue from sales from the next two months. Based on the provided information, how many constraints does this problem have excluding the non-negativity constraints?Tennis Products, Inc., produces three models of high-quality tennis rackets. The following table contains recent information on the sales, costs, and profitability of the three models: Average Quantity Current Total Variable Cost Contribution Margin Contribution Sold Price Revenue Per Unit Per Unit Margin* Model (Units/Month) ($) ($) ($) ($) ($) 15,000 30 450,000 15.00 15 225,000 В 5,000 35 175,000 18.00 17 85,000 10,000 45 450,000 20.00 25 250,000 Total $1,075,000 $560,000 *Contribution to fixed costs and profits. The company is considering lowering the price of Model A to $27 in an effort to increase the number of units sold. Based on the results of price changes that have been instituted in the past, Tennis Products' chief economist estimates the arc price elasticity of demand to be -2.5. Furthermore, she estimates the arc cross elasticity of demand between Model A and Model B to be approximately 0.5 and between Model A and Model to be approximately 0.2. Variable costs per unit are…
- 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.21. Maximum revenue and profit. A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are C(x) = 72.000 + 60x P3D200 0 < x < 6,000 30 (A) Find the maximum revenue. (B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set. (C) If the government decides to tax the company $5 for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge company for each set?Pre-mixed concrete is an important input for the construction industry. Concrete cannotbe stored or transported over long distances as it begins to set after only a few hours. Forthis reason, only the three local firms—Aggregate Inc., Big Industries and ConCorp—arein a position to compete in the market. Moreover, the capital and regulatory requirementsfor constructing a new concrete plant are substantial, creating an effective barrier to entry.Pre-mixed concrete is regarded as a homogeneous good by the construction industry.Inverse demand in the market has been estimated to be,P = 600 −Q/50,where P represents the price of a cubic metre of concrete in dollars, and Q is the totalnumber of cubic metres of concrete supplied into the market on a given day.At present the three firms appear have identical production costs, with each firm facingfixed costs of $400,000 per day and a marginal cost of $180 per cubic metre.Big Industries and ConCorp estimate that the proposed merger would reduce…
- 7. A paint store sells 270 pails of paint per month at a price of $32 each. A customersurvey indicates that for each $1.20 decrease in price, sales will increase by 6pails of paint.(a) Determine the demand, or price, function.(b) Determine the revenue function (using (a)).(c) Determine the marginal revenue function.(d) Solve R’(x) = 0. Interpret the meaning of this value for this situation.(e) What is the price that corresponds to the value found in part (d)?QUESTION 14 28 24 20 16 12 8 4 0 P 0 4 8 12 16 20 S1 D1 24 Q 14. The maximum that buyers are willing to pay for the 16-th unit of this product is O a) $2 O b) $4 c) $8 O d) $10 e) $12Q)Firm A and B are Cournot competitors, who produce good x. Both firms have zero cost and demand is X = 215 – P, where P is market clearing price. If firm produces 90 units, then what is the optimal amount of output for firm A to produce. solve our if you know correct and clearsolution.
- A steel firm creates water pollution for a downstream fishery. The price and cost functions for steel and fish are as follows: Price of steel 30 Cost function for steel Csteel(s,x) 6s + 3s? – 20x + 2x² Price of fish 50 Cost function for fish Cfish(f,x) 20f+5f² + 14x +x? (a) How much steel (s), pollution (x) and fish (f) will the steel and fish plants produce if they are merged and act to maximize joint profit? (Maximise joint profit)5- A manufacturer of doors, windows, and cabinets writes her yearly profit (in thousands of dollars) for each category in 248 a vector as: P= 319 632 40 30 Her fixed costs of production can be described by the vector:C- 60 What would her incomebif increasing it threefold would cause her profit to be fice times as arger 513,02 421; 623 427 72 907: 03 542 513,02 007;23 542 542: 3 007 421: 23 513Problem 1 A lash adjuster keeps the pressure constant on engine valves, increasing automobile engines' fuel efficiency. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D=(2,000-p)/0.10. 6 a) What is the demand (D) when total revenue is maximized? b) What important data are needed if maximum profit is desired? & 7 IAA fg 8 DII myhp np f10 DDI 9 fi Po 112 prt sc