The total profit equation for the firm is p =-500-25x-10x^2 -4xy-5y^2+15y ;x +y =100 .where x and y represents output levels.Us8ng substitution method determine the profit maximizing output levels for x and y .
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- Question 1 A computer retailing company specializes in the sale of jump drives to community college students The demand function for jump drives is p=2x- +10=1000 dollars For the samne company the average cost function is given as. 2+36v-1600 - dollars Where pis the price n dollars and x represents units ofiourput. Determine the revenue function Determine the cost funetion Determine the profit function Find the price and output that will maximıze profir, Find the maximum profit 11 111) Iv) Ouestio n 2On 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_________.Эшestion 1 A computer retailing company specializes in the sale of jump drives to community college tudents. The demand function for jump drives is p=2x+10x+1000 dollars For the samne company the average cost function is given as: ē = 2x +36x-1600- 20 * dollars Where p is the price in dollars and x represents units of output. 1) i1) Find the price and output that will maximize profit. Find the maximum profit
- A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (d) How many laundry sinks will the company need to produce in order to maximise it′s profits?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 functionRoad 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…
- X 1 ences If the price of oats is $3.0 per kilo, calculate the total revenue and the total profit (or loss) at the quantities shown in below table. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Leave no cells blank - be certain to enter "0" wherever required. Mc Graw Hill Quantity (kilos) Total revenue Total cost Total profit $ 600 1800 $1,900 700 2100 $2,000 $ 800 2400 $2,400(a) The marginal cost of two firms are given by the following | cost Firm 1: C'(Q) = 300e® 1Q+2 TC= 3000 when Q = 0 Firm 2: C'(Q) = 41 +30Q -5Q² TC =400 when Q = 0 (ii, (iii) avee (iv) Find the total cost for producing up to 100 unitsA 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…
- 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) 250 225 200 175 150 125 100 75 50 25 0 0 5 10 Demand 15 20 25 30 35 40 45 50 QUANTITY (Units) Graph Input Tool Market for Goods Quantity Demanded (Units) Demand Price (Dollars per unit) 25 125.00 ?The marginal revenue from the sale of x bottles of fancy sparkling water is given by R' (x) 84 0.03 x dollars per bottle. Find the increase in total revenue if the number of bottles sold increased from 225 to 350 5.A company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500 per day when producing 15 sinks. The company has a daily demand function of q = 360 − p, where q is the number if laundry sinks demanded and p is te price of a laundry sink. (e) What is the maximum profit?