Thingamabob Sales Yaster Inc. is trying to enter the thingamabob market. The research department established the following price-demand, cost, and revenue functions: Price- |p(x) = 57 – 1.14x demand function |C(x) = 215 + 11x Cost function Revenue |R(x) = xp(x) = x(57 – 1.14x) function where x is in thousands of thingamabobs and C(x) and R(x) are in thousands of dollars. The price p(x) is the price in dollars of one thingamabob when the demand is a thousand thingamabobs. All three functions have domain 1≤ x ≤ 50.
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- On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 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. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.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…|1.6.1 A company manufactures and sells x dellphones per week. The weekly price-demand and cost equations are given below. p= 400 - 0.5x and C(x) = 20,000 + 140x (A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly revenue is $ (Round to the nearest cent as needed.) (B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit? The company should produce (Round to the nearest cent as needed.) phones each week at a price of $ The maximum weekly profit is $ (Round to the nearest cent as needed.)
- A donut shp has a fixed cost of $92000 per day and a varibale cost of $2 for each donut produced. If the donuts are sold to distributors for $5 each. What is the price-demand function? What is the revenue function?Suposse a munufacture of widgets has a fixcost of $2500, a variable cost of $30 per widget ans sell 100 widgets for 4,500. Find the cost function C(n) Find the revenue function R(n) Find the profit function P(n)Find average revenue if total revenue is $4400 and output is 22
- Suppose the marginal cost and marginal revenue (in ¢000) for a product produced by a company is estimated to beMC=q+35 MR=560+22q−q2Where q is the quantity produced and the firm’s break-even is 5 units per weekYou are Required to1. determine the total cost and the total revenue function in terms of q.2. estimate the output at which profit is maximize3. calculate the maximum profitThe 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)…Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Required. Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market.? 2. Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging thesameprice in the two markets what are the profit…
- What is the demand function and cost function based on the set of data below? Price Quantity Profit $50 88 -$240 $25 289 -$240 $80 -$2000 $52 148 $1256 $51 143 $1003 $55 103 $575Question Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets,Bangladesh and Sri Lanka. Demand for Bicycles in thesetwo markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) Now consider two cases (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits? c. Analyze, with graphs, the two alternative pricing strategies…A startup software company has indicated its cost, c(x), and revenue, f(x), as given below, such that x is the number of lines of programing code (units in 1000 lines). c(x) = 80000 - 2(x-200)2 f(x) = (x-10)3 + (x+10)2 Find the marginal cost analytically, and draw its graph Find the marginal revenue analytically, and draw its graph Solve for the x point where marginal cost is equal to marginal revenue analytically. Comment why is this point significant analytically. Write the profit function and draw its graph Is the profit function concave up or concave down?