A demand curve is given by p = 660-3x. Assume you must pay salaries totalling 8000$ in a month. Also, it costs $110 to manufacture one TV. Graph the profit function, M(x)=550x-3x²-8000, and using the Maximum program, find the maximum possible profit and fill in the details (round off x to the nearest whole number): revenue:
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We are going to use Single variable maximisation method to answer this question.
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- Let 10p + x = 100 be the demand equation, where p is the price per item when x items are demanded. (a) Find the total revenue when the level of production is: (i) 40; (ii) 41; (b) Find the exact revenue derived from the 41st item. (c) Find the approximate revenue derived from the 41st item. (d) What is the error if the derivative is used to approximate the marginal revenue?The total cost function will be given by Total Cost = 200 + 2Q + 0.01 Q^2 and demand function is Q = 1000 - 0.02 p, where p is a price. Find the demand Q at which Total net benefit is maximized. Find the associated values of price, total net benefit, profit, and consumer surplus.The demand function for small high-definition televisions is given by p = 9,000 − 55x, where p is the price, in dollars, that x televisions can be sold. The cost function (in dollars) to produce televisions is C = 3,500x + 2,000. (Simplify your answers completely.) (a)Find the revenue function, R. R = (b)Find the profit function, P. P = (c)Find how many televisions should be sold to maximize profit. televisions (d)What is the maximum profit (in dollars)? $
- I need some help and can you show me all the steps, please The profit of a firm is described by the following function: f(Q) = -8Q^3 + 30Q^2 – 120Q – 100 where Q is the quantity produced. (A) Find the stationary points for this function. (B) Using the first derivative test, find for what value of Q the profit maximised. (C) Find the feasible values of Q where the graph of the profit function is concave up.Question A Suppose the short-run production function is q = 1L0.5. If the marginal cost of producing the 10th unit is $8, what is the wage per unit of labor? Question B A consumer has the utility function U(q1,q2) = q10.5 + q2Assume p2 = 1 and Y = 100. What is the equivalent variation of a price increase for good 1 from 1 to 4?Elsie sells homemade lemonade. If she prices a glass of lemonade at $3, she sells 12 glasses a day. If she gives a $0.50 discount (per glass), she can sell 3 more glasses per day. Write a linear demand equation q = mp + b, where p is the price per glass, and q is the number of glasses she can sell per day. Suppose that it costs her 20 cents a glass to make lemonade. There is no fixed cost. Write down the revenue function, cost function, and profit function as functions of p. How much should she charge per glass to maximize her profit? What is the maximum profit?
- The daily cost to manufacture generic trinkets for gullible tourists is given by the cost function C(x) = −0.001x2 + 0.3x + 500 dollars where x is the number of trinkets. a. As x increases, the marginal cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. b. As x increases, the average cost(A) increases (B) decreases (C) increases, then decreases. (D) decreases, then increases. c. The marginal cost is(A) greater than (B) equal to (C) less than the average cost when x = 100.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 4(i) If the demand curve 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: 1. All values of x for which production of the commodity is profitable.
- MacGuffins have a demand function of QD = 70 – P and a supply function of QS = 2P + 10. Determine the supply quantity when the price is $40.A 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 unitFind the price that will maximize profit for the demand and cost functions, where p is the price, x is the number of units, and C is the cost. Demand Function p= 78-0.1 square root x Cost Function C = 33x + 550 $ =