Consider the following price-demand function: P = 80 − 4Q, {Q/0 ≤ Q ≤ 10} (i) Sketch the price-demand function (ii) Find the revenue function. (iii) Suppose C = 20 + 5Q , find the profit function (iv) Calculate the profit if Q=8 (v) Find the break-even level of output You have to solve iv and v
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Consider the following price-
P = 80 − 4Q, {Q/0 ≤ Q ≤ 10}
(i) Sketch the price-demand function
(ii) Find the revenue function.
(iii) Suppose C = 20 + 5Q , find the profit function
(iv) Calculate the profit if Q=8
(v) Find the break-even level of output
You have to solve iv and v
Step by step
Solved in 3 steps
- Consider the following price-demand function: P = 80 − 4Q, {Q/0 ≤ Q ≤ 10} (i) Sketch the price-demand function(ii) Find the revenue function.(iii) Suppose C = 20 + 5Q , find the profit function(iv) Calculate the profit if Q=8(v) Find the break-even level of output(i) If the demand function for a particular commodity is p=−0.09x+51 and the total cost function C(x)=1.32x2+11.7x+101.4,where x is the level of production. Find (a) The revenue R(x) and profit Π(x). (b) All values of x for which production of the commodity is profitable. (ii) The total cost of manufacturing x units during the daily production run at a factory,is C(x)= x2+ x+900 dollars. Usually,x(t)=25t units are manufactured during the first t hours of production. (a) Express the total manufacturing cost as a function of t. (b) How much will have been spent on production by the end of the third hour? (c) When will the total manufacturing cost reach $11,000?The price-demand equation for the production of bluetooth speakers is: p = 250 - 1/20x, for 0 is less than or equal to x and x is less than or equal to 5000 where x speakers can be sold at $p per each speaker. The cost to produce x speakers is given as C(x) = 150,000 + 30x, where both C(x) and p are represented in dollars ($). - find the profit function and the marginal profit and interpret the quantity P'(4500) - find the marginal cost and interpret the quantity C'(3000) - find the revenue function and the marginal revenue and interpret the quantity R'(3000)
- Suppose the demand function for a product is given by the function: D ( q ) = − 0.02 q + 80 D ( q ) = - 0.02 q + 80 Use integration (or other appropriate methods) to find the following: (Do no rounding of results until the very end of your calculations. At that point, round to the nearest tenth, if necessary. It may help you to sketch the demand curve, which crosses the horizontal at q = 4 , 000 q = 4 , 000 .) A) The total actual revenue for q = 3 , 350 q = 3 , 350 units: Answer 1: B) The total possible revenue (for all quantities and prices): Answer 2: C) The Consumer's surplus corresponding to q = 3 , 350 q = 3 , 350 units: Answer 3: D) The "Not Sold" value corresponding to q = 3 , 350 q = 3 , 350 units: Answer 4The demand function for a particular brand of LCD TV is given by p = 1480 − 20x where p is the price per unit in dollars when x television sets are sold. (a) Find the revenue function. R(x) = (b) Determine the number of sets that must be sold in order to maximize the revenue.sets(c) What is the maximum revenue? $ (d) What is the price per unit when the revenue is maximized?$ per unitA business sells items according to the following Cost and Revenue functions: C(x)=10x+6100Cx=10x+6100 R(x)=−3.5x2+340xRx=-3.5x2+340x (a) Find the profit function: P(x)=Px= (b) How many items should be sold to break even? (Round to the nearest whole number. Enter your answer as a comma-separated list if necessary) (Enter the smaller number first) x=x= (c) What is the maximum profit for this business? (Round to two decimal places)
- Assume you are the manager of a firm that produces a unique pair of rainbow shorts. Based on the estimates provided by a consultant, you know that the relevant demand and cost functions for these shorts are Q=100−2P; C=40+2Q2.What are the levels of quantity and price when you are maximizing profits?The marketing research department for a company that manufacturers and sells gaming systems established the following price-demand function p(x)=240-30x Where p(x) is the wholesale price in dollars at which x thousand gaming systems can be sold, Find the revenue function when x thousand units are demanded Find the value of x that will produce maximum revenue. What is maximum revenue to the nearest thousand dollars? What is the price per gaming system that produces the maximum revenue?Example 2:Management has at its disposal the following information:Demand (price) function: P =32 –QTotal cost function: C(Q) = 200 +2Q.Using the above functions, determine the following:a. Profit maximizing output (quantity)b. Profit-maximizing pricec. Maximum profit valued. Revenue-maximizing output. (quantity)
- please solve question 4- Prove that total revenue is maximized for a linear demand function, P = a - bQ point where Q = a / 2 * b . - Minimize the following cost function: TC = 1/3 * Q ^ 3 - 8.5Q ^ 2 + 60Q + 27– A certain cleaning company cleans professional offices and believes its staff can clean up to 300 office units a week at a labor and supply cost of $58 per unit. Preliminary pricing surveys indicate that if that if the company charges $100 per unit, it will have clients for 300 units. For every $5 price increase it can expect a demand of 10 fewer units. Assume the demand, s, is a linear function of price p. Find an equation for demand as a function of price. Find the Revenue and Cost functions, both of which are dependent on price p. Write the Profit function. Using Desmos, graph the Revenue, Cost, and Profit functions on the same coordinate plane. Label the axes and the functions and use an appropriate scale. Find the break-even points graphically and confirm algebraically. Label the regions of profit and loss on the graph. Algebraically find the price that results in a maximum profit. Conclusion: A price of $_________ results in a quantity of _____________ units…If demand function is given as the following: Qz = 230 -2.75 Pz + 0.5 I + 1.2 Pm + 0.6A Where Qz is quantity of Good z sold, Pz is price of Good z per unit, I is per capita income, Pm is price of competitor and A is the amount of advertising spent. Current values: Pz= RM 55 I= RM 9000 Pm= RM 50 A =RM 12,000 a) Should the firm consider giving a price discount in order to increase total revenue?