A consultancy firm, focusing on capacity building in Research Methodology has a demand function Q = 10 – 0.1P where cost per unit function as 400 Q-8+ Where Q is the number of capacity building hours and P is the price per hour. a) Determine the number of capacity building hours which maximizes the company's profit. b) How much should the rm charge for the capacity building? c) Find the total profit at the profit maximizing level of consultancy. d) Using the own price elasticity of demand. e) Comment on the firm's pricing policy options.
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- The economic analysis division of Mapco Enterprises has estimated the demand function for its line of weed trimmers as QD=18,000+0.4N350PM+90Ps where N=numberofnewhomescompletedintheprimarymarketarea PM=priceoftheMapcotrimmerPS=priceofitscompetitorsSurefiretrimmer In 2010, 15,000 new homes are expected to be completed in the primary market area. Mapco plans to charge $50 for its trimmer. The Surefire trimmer is expected to sell for $55. What sales are forecasted for 2010 under these conditions? If its competitor cuts the price of the Surefire trimmer to $50, what effect will this have on Mapcos sales? What effect would a 30 percent reduction in the number of new homes completed have on Mapcos sales (ignore the impact of the price cut of the Surefire trimmer)?A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week. a.What is the optimum number of units the defense contractor should produce in order to maximize profit per week? b.What is the profit if the optimum number of units are produced?A local defense contractor is considering the production of fireworks as a way to reduce dependence on the military. The variable cost per unit is $40D. The fixed cost that can be allocated to the production of fireworks is negligible. The price changed per unit will be determined by the equation p=$180-(5)D, where D represents demand in units sold per week. a.What is the optimum number of units the defense contractor should produce in order to maximize profit per week? b.What is the profit if the optimum number of units are produced? Show handwritten solutions
- A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 − 0.01 × Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing) = $50,000 and the variable cost per unit = $40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 6,000 units per year.The manufacturer of smart printers is trying to decide what price to set for its product. The demand and cost function are assumed to be as follows: P = 80 -2Q TC= 160 +50Q-1.5Q ² What price should the company charge if it wants to maximize its profit in the short run? What is the optimal quantity for the printer following this optimal price?Using a linear specification, you estimate your demand curve to equal Q=20-2P+10I, where • Q = the quantity demanded of your product • P = the price of your product • I = customer income (measured in thousands of dollars) In addition, your operations team estimates you have a constant marginal cost of $10. What quantity should you set to maximize profits assuming your average customer income equals $18000 (i.e. I=18)? a. Q=45 b. Q=50 c. Q=55 d. Q=90 e. Q=180
- Q1. Game console manufacturing determines that in order to sell Q units, the price per unit (in dollar) must decreased by the linear demand (the demand function) P(Q)= 800- 0.3Q($/device) The manufacturer also determine that the cost depends on the volume of production and includes a fixed part 500,000($) and a variable part 500Q , that is C(Q)= 500000+ 500Q What price per unit must be charged to get the maximum profit?– 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…denton productions limited utilizes statistical analysis to determine the optimal price for its sales to customera, during july 2020, the company was provided with the following demand and cost functions by a statistical research company, p=200-6Q, where p=price in dollars; and Q=quantitity of units in thousands TC=5Q2 + 24Q + 150, where TC is total costs in thousands of dollars a. determine the optimal output for july 2020 b. find the price that maximized profit
- A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price=160−0.02×Demand for an annual printing of this particular product. The fixed costs per year (i.e., per printing)=$47,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 4,000 units per year. The maximum profit that can be achieved is $? (Round to the nearest dollar.) The unit price at the point of optimal demand is $? per unit. The manufacturer of smart printers is trying to decide what price to set for its product. The demand and cost function are assumed to be as follows: P = 80 -2Q TC= 160 +50Q-1.5Q ² What price should it charge if it wants to maximize its revenue in the short run? What is the optimal quantity for the printer under this price? No handwriting. Please. TypeA company produces and sells a consumer product and thus far has been able to control the volume of the product by varying the selling price. The company is seeking to maximize its net profit. It has been concluded that the relationship between price and demand, per month, is approximately D = 500 – 5p, where p is the price per unit in dollars. The fixed cost is $1,000 per month, and the variable cost is $20 per unit. Obtain the answer mathematically to the following questions: a.What is the optimal number of units that should be produced and sold per month? b.What is the maximum profit per month? c.What are the breakeven sales quantities and the range of profitable demand volume?