A firm has found from past experience that its profit in terms of number of units x p a) Find the value that maximizes the profit. b) Find the maximum profit. c) show that your answer in part (a) has been maximized, (Upload the picture of your solutions)
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- After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.Cost, revenue, and profit are in dollars and x is the number of units. A firm knows that its marginal cost for a product is MC = 2x + 20, that its marginal revenue is MR = 44 − 6x, and that the cost of production of 100 units is $12,160. the optimal level of production is 3 units. a) find the profit function b) Find the profit or loss at the optimal level.Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. Therefore, at a production level of 200 cups of ice cream, the revenue generated by the company would be $130 for each additional cup of ice cream produced. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (a) Find the value(s) of x at the break-even points. (b) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.
- It is known that the demand function for a good is shown by the equation P = - 5Q + 110 and the total cost of production is C = 100 + 10Q + 5Q². Calculate the maximum profit rate of sales, the amount of profit and the selling price per unit.A company has determined that its prodor for a product can be described by linear function. The profit from the production and sales of the 150 units is $455, and the profit from 250 units is $895 1. What is the average rate of change of the profit for the product when between 150 and 250 units are sold? 2. Write the equation of the profit function for this product? 3. How many units give break-even for this product?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)
- 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 Develop the nonlinear profit function for this company and determine the price that will maximize profit, the optimal volume, and the maximum profit per month.A company finds that it can sell out a certain product that it produces, at the rate of Tk. 2 per unit. 1 It estimates the cost function of the product to be Tk. 1000 + 2 50 for q units produced. (i) Find the expression for the total profit, if q units are produced and sold. (ii) Find the number of units produced that will maximize profit. (iii)What is the amount of this maximum profit? (iv) What would be the profit if 6000 units were produced?You are the manager of a firm and you are required to optimize the Cobb Douglas function given the following parameters. The maximum amount of money available is $1600 where the price of K = 12 and the price of L=6. That is PK=12 and PL=6. The function is given as q=K0.4+L0.6. What are the optimal values of K0 and L0?
- Refer to the figure below to answer the questions. 1.) A corn producer's profit is RM200 and is producing 100 bushels of corn. Then he must have a cost per bushel of __________. 2) A corn producer produces 80 bushels of corn and sells each bushel at RM5. The cost of producing each unit bushel is RM2. This corn producer's total revenue is ________ and profit is ________. 3) A corn producer's total revenue is RM1,000. If she sells each bushel of corn for RM5, she must be selling ________ bushels of corn.You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the following parameters. The maximum amount of money available to spend is $340 where the price of K=8 and the price of L=4. That is Pk=8 and Pl=4. The function is given as q=K0.4L0.6 . What are the optimal values K0 and L0 ? a. None of the above b. K0≈68,L0≈34 c. K0≈72,L0≈18 d. K0≈34,L0≈68Revenue from product X is $11,000, variable costs are $7,000, and allocated fixed costs are $6,000. If you drop product X in the long term, profit will: