1. A company manufactures and sells x television sets per month. The monthly cost and price-demand equation are C(x) = 72,000+ 60x p=200-. X 30 a) Write the Revenue and Profit functions, and determine their domain. b) Sketch a careful graph of the Revenue and Cost functions (the domain of the functions must be clearly indicated on the graph). On the graphs, indicate where the break-even points are and the production levels (values of x) that result in profit, and the ones that result in loss.
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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_________."The Hickory Cabinet and Furniture Company makes chairs. The fixed cost per month of making chairs is $7,500, and the variable cost per chair is $40. Price is related to demand, according to the following linear equation: v = 400 - 1.2p Graphically illustrate the profit curve developed . Indicate the optimal price and the maximum profit per month.Consider total cost and total revenue given in the following table: TABLE IN IMAGE Calculate profit for each quantity. How much should the firm produce to maximize profit?(ii) Calculate marginal revenue and marginal cost for each quantity. Graph them. (Hint: Put the points betweenwhole numbers. For example, the marginal cost between 2 and 3 should be graphed at 2½.) At what quantitydo these curves cross? How does this relate to your answer to part (a)?(iii) Can you tell whether this firm is in a competitive industry? If so, can you tell whether the industry is in along-run equilibrium? (8.75)
- 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)…Jasmine decides to make and sell jelly cups. It costs jasmine Rs.1000 to set up and Rs.50 per cup made. She decides to sell each cup for 150. By using this information, answer the following questions: A) Write and equation for jasmine's revenue, cost and profit functions? B) Graph each function on a set of axes? C) Find the breakeven point from these graphs? ( D) How many jelly cups will jasmine need to sell in order to make a profit? (E) If jasmine wishes to make a profit of 50, how many jelly cups does she need to sell?The figure shows graphs of the total cost function and the total revenue function for a commodity. (Assume cost and revenue are measured in dollars.) y 500 400 300 200 100 MR 10 (a) Label each function correctly. function A ---Select--- function B ---Select--- (x, y): = 20 (b) Determine the fixed costs. $ 30 (c) Locate the break-even point. -([ = 40 50 Determine the number of units sold to break even. units A B 60 (d) Estimate the marginal cost MC and marginal revenue MR. MC = X
- 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 functionQ3) the demand function and total cost function for a product are 6P = 660 − 3Q, TC = 80 − 20Q2 + 600Q (a) Write down expressions for: (i) Average cost, (ii) marginal cost, (iii) total revenue, (iv) Marginal revenue, (v) Profit. (b) Determine the values of Q for which total cost is a maximum. Calculate the maximum costs. Calculate the profit when total costs are a maximum. (c) Determine the value of Q for which profit is a minimum. What is the minimum profit?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…
- 14.The demand function for a new product is p(x) = - 2x + 7 , where p is the selling price of the product and x is the number sold in thousands. The cost function is C(x) = x + 2 . a) Determine an equation for the profit, in standard form and in function notation. b) How many units must be sold for the company to break even?1. Suppose the total cost to a firm of producing a quantity ą of some commodity is C(q) = 490 + 20q + 0.1q² dollars. a) Find the corresponding marginal cost (MC(q)) and average cost (AC(g)) b) Find the minimum average cost and the output level at which it is achieved c) Verify that MC(q) = AC(q) at this output level you found in section “b)"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) $