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- A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. 1) What is the company’s range of profitable output per year?A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be: p=10-(42/D^2)+2Dwhere p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month.a) Derive how to find the number of units that should be produced annually to maximize profit.b) What is the maximum profit per year?c) What is the annual breakeven point?d)What is the company’s range of profitable output per year?nd 35. AVERAGE SUPPLY A manufacturer supplies S(p) = 0.5p² + 3p + 7 hundred units of a Sie per certain commodity to the market when the price is p dollars per unit. Find the average supply as the price varies from p = $2 to p = $5. 6 43. E
- Redleaf company's market research department works on the manufacture and marketing of a winter tire for vehicles. Currently the price is 10$, and the demand is 13000 units. When the price is increased to 15$, the company expects the demand to be 8500 units (assume that price is linearly related to demand.). Company is following a make-to-order policy for their production, meaning that they make production as much as ordered from their dealers. The dealers make orders 3 times a year, on January, May and September. The company has 23 dealers, who do not have any capacity restriction on their orders. Yet, the above information is a country-wise research, and shows the aggregate demand (sum of all dealers' orders) for each price. Regardless of the production amount, the company faces with a 2170$ of administrative cost for production, in addition to 1,3 $ cost of raw materials and labour costs per each units produced. If we define price as a function of demand (P(d)) using the…A manufacturer produces bolts of a fabric with a fixed width. The quantityqof this fabric(measured in yards) that is sold is a function of the selling pricep(in dollars per yard), sowe can writeq=f(p). Then the total revenue earned with selling pricepisR(p)=pf(p).A firm has an annual demand of S units for a good whose purchase cost is £c per unit. Each order costs £a to place, and the cost of holding stock is b% of the average value of stock per annum. Determine the optimal order quantity. A local firm uses 2000 units of a particular component each year. The component has a purchase price of £4/unit, while the cost of holding stock is estimated at 20% of the average stock value. If the cost of placing each order is £12.50, find the optimal number of orders placed each year. Suppose the component supplier offers a discount of 2% on the purchase price if orders are placed in units of 1000. Is the discount worth accepting? Suppose that instead of a single figure you had been given a probability distribution for the number of units used each year. Indicate the effect on stock policy.. Please explain fully , the last part is also important to solve.
- FG Manufacturers wants to determine the effectiveness of their pricing decisions for their product Lylo. As a consultant, you have been asked to develop cost functions that will assist in arriving at the optimal price that will enable the company to maximize profits. During the year, you were provided with the following demand and costs functions for the product: P = 400 – 6Q; where P is the unit selling price and Q is quantity in thousands of units. TC = 8Q2 + 36Q + 150; where TC is total cost in thousands of dollars. Determine the optimal sales revenue. Calculate the maximum profit. Briefly outline two (2) factors to be considered by managementswhen pricing decisions are being made.A small countertop installing company hires you to estimate their customers weekly demand function for marble (per sq ft). The demand function is as follows: Qm=5000-30Pm +20Pg + 0.05Inc m=marble, g= granite, inc = avg disposable income for home improvements in the surrounding area. Current prices: marble = 40, granite = 25 and disposible income = 5000 Suppose during the supply change shortage the price of marble triples to $120 Determine the elasticity of demand at the new market price for marbleProblem 2 Refer to problem 1.(Problem 1: Auto Mart is a mythical seller of a variety of automobileparts and accessories. Auto Mart's owner, Jonathan Trott, wishes to determine the optimum order quantity for oneof the store's popular wiper blades. The annual demandfor the wiper blades is 16,000. The annual holding costper unit is US$2.50, and the cost to place an order is US$50:) Assuming that holding costs and ordercosts remain the same, if annual demand for wiper blades doubles to 32,000, does the EOQ also Double? Explainyour answer with relevant calculations.
- Currently, the exchange rate is 100 yen per dollar. InJapan, we sell a product that costs $5 to produce for 700yen. The product has an elasticity of 3. For exchange ratesvarying from 70 to 130 yen per dollar, determine the optimalproduct price in Japan and the profit in dollars. Assume alinear demand curve. Current demand is assumed to equal100.TIME Qd Price 1 44 10 2 40 9 3 42 11 4 46 12 5 48 11 6 52 12 7 54 13 8 58 13 9 56 14 10 60 15 Estimate demand as a function of price and shoew the line of best fit What would happen to the demand if price is Taka 20?Agnes, a General Manager in XXX Company, estimated a multiplicative demand function of the form: using a cross-section data collected in the company sales on 30th June, 2019. The estimation results are as follows: Constant Price(P) Income (I) Price of other Good (Po) Estimated coefficient 0.022 -0.223 1.354 0.133 Standard Error 0.012 0.056 0.502 0.814 t-statistic (1.19) (-3.98) -2.69 -0.13 Number of Observations, n=210; R-squared= 0.7516 Critical Students t=1.96 at 5% Level of Significance Write down the estimated demand equation Interpret the coefficients and value Describe any three managerial decisions that can be applied by the manager from the estimated demand function