A company's revenue and cost function is given by R = 80Q – Q? and C = 55 – 120Q + Q? respectively. (a) Determine the level of output that maximises the profit. (b) Determine the price elasticity of demand at the level of output that maximises the profit. Comment on the answer found.
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A: a)TR(Q)=500Q-13Q3Now,MR=∂TR∂QMR=∂(500Q-13Q3)∂QMR=500-33Q3-1MR=500-Q2
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- The demand function for FreshFood Exclusive Brand's product is D = 80 - 2p , where D is the number of units and 'p' is the price per unit. The value of D that will achieve maximum revenue is __________________.The price/demand function of a company is p=42-0.001D and the cost function is 30D+1200. Determine the following: The optimal demand = The optimal value = The demand that will give the highest revenue = The highest revenue value = Breakeven Points = Range of Profitability =The demand function for a firm's product is q= 500+50p where q equals the number of unit demanded and p equals the price in dollars a) Determine the price which should be charged to minimize total revenue b) what is the maximum value for total revenue?
- 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. A manufacturer of a new patented product has found that he can sell 70 units a week to the customer if the price is $48. In error, the price was recently advertised at $78 and as a result only 40 units were sold in a week. The manufacturers fixed costs of production are $ 1710 a week and variable costs are $9 per unit. You are required to Recommend a unit price which would maximise profit and to find the quantity demanded and profit generated at that price.Many times, the selling price of a product, p, is related to the demand, D, according to the relationship p=a-bD. However, a company has found that the price of their product can be related to demand ( in units per year) according to the following equation: p= $88.5 – (0.5)D0.5 . In addition, there is a fixed cost of $20,000 per year and the variable cost to manufacture the product is $20 per unit. a. What level of demand maximizes total revenue and the maximum revenue? b. What level of demand maximizes total profit for this product and the maximum 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 = 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.Short Grass Incorporated is a distributor of golf balls. Martin's Golf Supplies is a local retail outlet which sells golf balls. Martin's purchases the golf balls from Short Grass Incorporated at $1.15 per ball; the golf balls are shipped in cartons of 72. Short Grass Incorporated pays all incoming freight, and Martin's Golf Supplies does not inspect the balls due to Short Grass' reputation for high quality. Annual demand is 159,520 golf balls at a rate of 3,691 balls per week. Martin's Golf Supplies earns 10% on its cash investments. The purchaseminus−order lead time is one week. The following cost data are available: Relevant ordering costs per purchase order $132.00 Carrying costs per carton per year: Relevant insurance, materials handling, $0.87 breakage, etc., per year What is the economic order quantity? (Round costs to the nearest cent and quantities to the nearest whole number.)A toy manufacturer makes miniature trucks. The price p (in dollar) and the demand x (number of miniature trucks) are related by the equation 6000 − 600p = x. The total cost for the same toy manufacturer to produce x miniature trucks can be modeled by C(x) = 8x + 450.a) Find P' (300) and interpret the result.b) What is the exact profit from the sale of the 301st miniature truck?