The inverse demand function of a certain product is represented by p=4350-13q. Suppose the firm faces an average cost function for producing each unit of the product of AC=q²-5.5q+150. Find the output level, q, that would maximize this firm's profit, z. Verify if the maximization condition is met. If so, how much is the maximum profit?
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- Q: determine whether the following statements are true or false: a) Average fixed costs increase when the total volume of the produced goods increases. b) If the market price is constant, the increase in output will not affect the size of the firm's profit.Assume that a firm’s marginal revenue curve intersects the rising portion of its marginal cost curve at 500 units of output. At this output level, a profit-maximizing firm’s total cost of production is $1,000. If the price of the product is $5 per unit, the total revenue earned by the firm will be:(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?
- 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. Find the profit-maximising level of output using the profit function and calculate how much profit is made at this output level.A firm has a linear demand function for it's product.When the price for the product is Sh.220,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 given by; MC = 40Q-2Q^2+2 Fixed cost = Sh. 5 million Where Q= quantity demanded, Mc= marginal cost(cost in Sh. Million) Required 1.The level of output that maximises profits 2.The maximum profit 3.The price of the product at a maximum profitA commodity has a demand function modeled by p = 106 − 0.5x and a total cost function modeled by C = 30x + 33.75, where x is the number of units. (a) What unit price (in dollars) yields a maximum profit? $ per unit (b) When the profit is maximized, what is the average cost (in dollars) per unit? (Round your answer to two decimal places.) $ per unit
- A firm has a price of 18$ per unit for its products while it has a variable cost of VC = q2 + 2q where q is the level of output. In addition the firm has a fixed cost of 20$. a. Write the profit function b. Calculate the level of output which will maximize the profit c. Show that the critical (stationary ) point is a maximum point rather than a minimum. d. At this output level, what is the total profit?A firm manufactures two goods labeled 1 and 2. It sells Qi items of good i for a fixed price per unit of pi. The total cost of producing good i is ciQi2.Explain briefly why the profit function is given byπ(Q1, Q2) = p1Q1 + p2Q2 − c1Q12 − c2Q22Find the values of Q1 and Q2 which maximize π and verify that the second-order conditions for a maximum are satisfied. Find an expression for the maximum profit.1) There are 1000 pear producers that have identical cost functions, where q is the number of crates of pear produced. The producers operate in a perfectly competitive market. The supply curve of each producer is _______ The total supply curve for the market is _______ At a price of 100, the elasticity of supply for the market is _______ , meaning that supply is _______. (see image for answer options) 2) A firm can sell its output at the price p=10 per unit. The firm’s cost function is C=16+q2 To maximize its profit, the firm chooses to produce q=___________. The profit of this firm is $_____________
- 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 profitSuppose that Quality Widgets Limited is an efficient small firm with cost functionC(q)=q3 - 10q2+100q + 196 and suppose also that the maximum level of weekly production is L=10. Determine:(d) their breakeven point, (e) their supply set.if the total revenue and total cost of a business are given by the following functions. what is the quantity that this business break even TR=2q^2+200q+2200 TC=-q^2+100q+100