A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Use equation (1) to find the total revenue (TR) function and determine the total revenue maximising output. Calculate the profit associated with this level of output.

A firm's demand and total cost function are given by the expression: P = 20 - Q/2 (1) TC = 0.5Q2 + 36 (2) Where P is price per unit in £ TC = total cost in £ Q is quantity demanded and produced. Use equation (1) to find the total revenue (TR) function and determine the total revenue maximising output. Calculate the profit associated with this level of output.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

See similar textbooks

Similar questions

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 textile company manufactures and sells x shirts per month. the monthly cost and price demand equations are given as C(x)= 150,000+30x and p = 50-x/100. using the analysis from obtaining the demand function and price elasticity of demand, discuss what the textile company can do to increase revenue from the sale of shirts.
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?
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?
The demand curve of a firm is p=1200– 21q and its total cost is C(q) = 2q – 66q² +600q+1000 where q is the output of the firm (in thousands). (i) Derive an expression R(q) for the firm' s revenue function. (ii) Derive an expression II(q) for the firm' s profit function. (iii) Is the rate of change of profit increasing or decreasing when the output level of the firm is 10,000 units?
Q2)Tony Keonte owns a factory that manufactures Eye-Games. His weekly profit (in thousands of dollars) is given by the following function: P(x) = -4x2 + 80x- 300. Where x is the number of Eye-Games sold. a) What is the largest number of Eye-Games that the company can sell and still make profit? (25 points) b) How many Eye-Games will the firm have to produce and sell in order to maximize profit? (25 points)
A firm's total revenue (TR) and total cost (TC) functions are TR = 110Q — 5Q2 TC = 10Q — O2 + 0.33Q3 Determine: a) Equations for marginal revenue and average revenue(b) Equations for marginal cost and the average cost (c) The output rate that maximize total revenue
At a price of R 8 per item consumers will buy 1500 units. If the company increases the price by R1 per item, the number of items that the consumers will buy will decrease by 75. i) Does the function described represent a supply or demand curve? Find the formula of the function given that it is a linear function. ii) Find the price that will maximize the revenue.
Let the demand function for a product be given by the function D(q) = - 1.3q + 290, where q is the quantity of items in demand and D(q) is the price per item, in dollars, that can be charged when q units are sold. Suppose fixed costs of production for this item are $5, 000 and variable costs are $9 per item produced. If 192 items are produced and sold, find the following: A) The total revenue from selling 192 items (to the nearest penny). Answer: $ B) The total costs to produce 192 items (to the nearest penny). Answer: $ C) The total profits to produce 192 items (to the nearest penny. Profits may or may not be negative.). Answer: $
Teddy J is a manufacturer of dish washing liquid . If his monthly demand function for 750mlsize is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q.(i) Derive an expression, R(q) for Teddy J′s total revenue curve.(ii) Derive an expression, Π(q) for Teddy J's profit function.(iii) Determine whether Teddy J′s profit is increasing or decreasing whenhe produces 5 hundred, 750ml bottles of dish washing liquid.(iv) How many 750ml bottles of dish washing liquid should Teddy J produceper month if he wishes to maximize his profits. thank you for your help
A firm has a linear demand function for it's product.When the price of the product is sh.20,the quantity demanded is 40 units.When the price increases to sh.240 the quantity demanded becomes 30 units.In addition,the firm's marginal cost function is giving by: Mc = 40q- 2q^2+2 Fixed cost = 5 million Where q= quantity demanded,Mc = marginal cost(sh.million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at the maximum profit
A firm's demand function is Q = 16 – P and its total cost function is defined as TC = 3 + Q +0.25Q 2 . Use these two functions to form the firm's profit function and then determine the level ofoutput that yields the profit maximum. What is the level of profit at the optimum?