0.2x The price-demand equation for the production of x ski jackets is given by: p = 200 1. Write the revenue function. 2. Find the total revenue when 80 ski jackets are produced and sold. F. Find the marginal revenue function.
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- 2. Firm A makes and sells motor cycles. The total cost of each cycle is the sum of the costs of frames, assembly and engine. The firm produces its own engines according to the cost equation C₁=250,000 + 1,000Q +5Q² The cost of frames and assembly is $2,000 per cycle. Monthly demand for cycles is given by the inverse demand equation: P = 10,000-30Q Calculate the MC of producing an additional engine.(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40−4q2where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit?(b) You are the CEO for a lightweight compasses manufacturer. The demand function for the lightweight compasses is given by p = 40 – 4q²where q is the number of lightweight compasses produced in millions. It costs the company $15 to make a lightweight compass. (i) Write an equation giving profit as a function of the number of lightweight compasses produced. (ii) At the moment the company produces 2 million lightweight compasses and makes a profit of $18,000,000, but you would like to reduce production. What smaller number of lightweight compasses could the company produce to yield the same profit? Problem з
- 11:30 l 4G I Homework 4 (section 2.1-2 & 2.2).pdf Economic Mathematics (1) Name ID Section 2.2 Revenue, cost and profit 1. If the demand function of a good is given by P-80 – 3Q, the fixed costs are 100 and variable cost are 5 per unit. Work out the profit when Q-10. 2. Find an expression for the profit function given the demand function 20+P= 25 and the 32 +5. Find the value of 0 for which the firm average cost function AC = (a) breaks even (b) makes a loss of 432 units (c) maximises profit. 2/2 !!3 Pierce Manufacturing determines that the daily revenue, in dollars, from the sale of x lawn chairs is R(x) = 0.003x° +0.01x +0.5x. Currently, Pierce sells 70 lawn chairs daily. a) What is the current daily revenue? b) How much would revenue increase if 75 lawn chairs were sold each day? c) What is the marginal revenue when 70 lawn chairs are sold daily? d) Use the answer from part (c) to estimate R(71), R(72), and R(73). ..... a) The current revenue is $ b) The revenue would increase by $. (Round to the nearest cent.) c) The marginal revenue is $ when 70 lawn chairs are sold daily. d) R(71) - $ R(72) $ R(73) $5. Demand functions are X-100-Px and Y=152-2Py Total Cost is C-6x2 + 4y2 +4xy + 110, Optimize the profit using two variable regular optimization formula.
- The graph below plots the firm's total revenue curve: that is, the relationship between quantity and total revenue given by the two right columns in the table above. The five choices are also labeled. Finally, two black lines are shown; these lines are tangent to the green curve at points B and D. 90 81 72 63 54 В D 45 36 27 18 A E 100 200 300 400 500 600 700 800 QUANTITY (Dishwashers per year) TOTAL REVENUE (Thousands of dollars per year)The blue curve on the following graph represents the demand curve facing a firm that can set its own prices. Use the graph input tool to help you answer the following questions. You will not be scored on any changes you make to this graph. Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly. PRICE (Dollars per unit) 100 TOTAL REVENUE (Dollars) 90 80 20 10 0 1250 1125 1000 875 750 625 500 On the previous graph, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 10, 20, 25, 30, 40, or 50 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. 375 250 125 + 0 0 0 Demand 5 10 15 20 25 30 35 40 45 50 QUANTITY (Units) + 5 20 10 15 25 30 35 QUANTITY (Number of units) 40 Graph Input Tool Market for Goods 45 50 Quantity Demanded (Units)…A local company is planning to manufacture and market a four-slice toaster. For this toaster, the research department’s estimates are aweekly demand of 300 toasters at a price of $25 per toaster and a weekly demand of 400 toasters at a price of $20. The financial department’s estimates are fixed weekly costs of$5,000 and variable costs of $5 per toaster. a) Assume that the relationship between price ? and demand ? is linear. Use the research department’s estimates to express ? as a function of ? and determine the domain of the function. b) Using your knowledge from Finite Math, determine the Revenue function in terms of ?. c) Determine the Marginal Revenue at 2 different production levels for example 250 and 500 units. Interpret these results. (HINT: Consider what a positive or negative first derivative implies) d) Assume that the cost function is linear. Use the financial department’s estimates to express the cost function interms of ?. e) Determinethe Marginal costand interpret the…
- A local newspaper currently has 84,000 subscribers at a quarterly charge of $30.Market research has suggested that if the owners raise the price to $32, they wouldlose 5,000 subscribers. Assuming that subscriptions are linearly related to theprice, what price should the newspaper charge for a quarterly subscription tomaximize their revenue?a) Find the cost function (Hint: find slope and use point-slope form to find thecost function) b) Find the revenue function c) Find the maximum revenue d) Find the profit functionThe following graph shows the daily demand curve for bippitybops in Denver. Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve. Note: You will not be graded on any changes made to this graph. PRICE (Dollars per bippitybop) 240 220 200 180 160 140 120 100 80 8 60 40 20 0 mớ H + 0 9 18 27 36 45 54 63 72 81 QUANTITY (Bippitybops per day) * Demand 90 B 99 108 Total Revenue (?)Co Assignment Content 1) When the Price is $4 the quantity supplied of hats is 100. If the price changes to $6 dollars and the quantity supplied changes to 400, is the elasticity of supply elastic, inelastic or unit elastic? How did you reach that conclusion? 2) Why will economic profits for firms in a perfectly competitive industry tend to vanish in the long run? What about accounting AS 12