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- Hau Lee Furniture, Inc., spends 60% of its sales dollars in the supply chain and has a current gross profit of $10,000. Hau wishes to increase gross profit by $5,000 (50%). He would like to compare two strategies: reducing material costs vs. increasing sales. The current material costs and production costs are 60% and 20%, respectively, of sales dollars, with fixed cost at a constant $10,000. Analysis indicates that an improvement in the supply chain that would reduce material costs by 8.3% ($5,000/$60,000) would produce a 50% net profit gain for Hau, whereas a much larger 25% increase in sales ($25,000/$100,000) would be required to produce the same result. Now Hau finds its current profit of $10,000 inadequate. The bank is insisting on an improved profit picture prior to approval of a loan for some new equipment. Hau would like to improve the profit line to $25,000 so he can obtain the bank’s approval for the loanWhat percentage improvement is needed in the supply chain strategy for…You are the marketing manager of the Business Unit (BU) that produces polystyrene (which is an input to making lightweight rigid foam). The current Demand/Supply balance, as measured by the ICIS price, is $800 per ton of polystyrene. The BU has 2 plants and can produce a total of 1800 tons. At full capacity utilization, the BU’s average variable cost equals $1300/t and its average total cost equals $1700/t. Plant 1 has a capacity of 600 tons and a marginal cost of $900/t. Plant 2 has capacity of 1200 tons and a marginal cost of $1500/t. Due to exit of one competitor, you expect next year’s polystyrene ICIS price to increase to $1200. How much volume of polystyrene do you expect to produce next year, ifany? 2.What is your expected contribution margin for nextyear? 3. What is your expected profit for nextyear?You are the marketing manager of the Business Unit (BU) that produces polystyrene (which is an input to making lightweight rigid foam). The current Demand/Supply balance, as measured by the ICIS price, is $800 per ton of polystyrene. The BU has 2 plants and can produce a total of 1800 tons. At full capacity utilization, the BU’s average variable cost equals $1300/t and its average total cost equals $1700/t.Plant 1 has a capacity of 600 tons and a marginal cost of $900/t. Plant 2 has capacity of 1200 tons and a marginal cost of $1500/t. Due to exit of one competitor, you expect next year’s polystyrene ICIS price to increase to $1200. 1. How much volume of polystyrene do you expect to produce next year, if any? 2. What is your expected contribution margin for next year? 3. What is your expected profit for next year?
- Constrained Optimization A firm's total cost function is: C = 6x2 - xy + 10y2 + 30, subject to the production quota x + y = 34. Construct the Lagrange function and solve for the equilibrium values. Calculate the total cost. What is the equilibrium value of x? What is the equilibrium value of y? What is the equilibrium value of λ? What is the optimized value of cost? What is the value of the determinant of the bordered Hessian matrix? Based on the value of the determinant of the bordered Hessian matrix, comment on the optimized value of Cost. (Answer in one word.)ABC Company is the manufacturer of a low-noise air-purification system. Its current capacity is 10,000 units/month, but ABC received orders totaling 9,000 units each month. Currently, ABC sells its system at a price of $200 per unit, its fixed cost is $500,000/month, and its variable cost is $100/unit. Note that currently, half of ABC’s variable cost is materials, and the other half is labor cost (wages for workers). ABC wants to consider cutting its price by 10% to stimulate demand. If ABC expands its capacity, it will have to lease additional manufacturing machines, each of which will cost $20,000/month to lease and can add 1000 units to ABC’s capacity. All existing workers are already working full-time. So, if ABC expands production, ABC has to either pay existing employees for overtime (1.5 times the regular wages) or hire new workers, who are expected to be paid 90% of the hourly wage of existing workers but produce only 75% of the hourly output of existing workers. (a) What is…A small manufacturing plant makes three types of inflatable boats: one person, two-person,and four-person models. Each boat requires the services of three departments, as listed in thetable. The cutting, assembly, and packaging departments have available a maximum of 380,330, and 120 labor-hours per week, respectively.Department One-PersonBoatTwo-PersonBoatFour-PersonBoatCutting 0.5 hr 1.0 hr 1.5 hrAssembly 0.6 hr 0.9 hr 1.2 hrPackaging 0.2 hr 0.3 hr 0.5 hra) Calculate how many boats of each type must be produced each week for the plant tooperate at full capacity.b) Calculate how is the production schedule in part (a) affected if the packagingdepartment is no longer used.c) Calculate how is the production schedule in part (a) affected if the four-person boat isno longer produced
- Critics of command-and-control policy often argue that regulationsare costly to business and industry, yet cost-benefitanalyses (p. 94) repeatedly show that regulations bring citizensmore benefits than costs, overall. Each year the U.S. Officeof Management and Budget assesses costs and benefits ofmajor federal regulations of administrative agencies. Resultsfrom the most recent report, covering the decade from 2003to 2013, are presented in the table (shown are averages fromranges of estimates). Subtract costs from benefits, and enterthese values for each agency in the third column. Divide benefitsby costs, and enter these values in the fourth column. For how many of the agencies shown do regulations exertmore costs than benefits? For how many do regulationsprovide more benefits than costs?Critics of command-and-control policy often argue that regulationsare costly to business and industry, yet cost-benefitanalyses (p. 94) repeatedly show that regulations bring citizensmore benefits than costs, overall. Each year the U.S. Officeof Management and Budget assesses costs and benefits ofmajor federal regulations of administrative agencies. Resultsfrom the most recent report, covering the decade from 2003to 2013, are presented in the table (shown are averages fromranges of estimates). Subtract costs from benefits, and enterthese values for each agency in the third column. Divide benefitsby costs, and enter these values in the fourth column. What percentage of total benefits from regulations comesfrom EPA regulations? Most of the benefits and costs fromEPA regulations are from air pollution rules resulting fromthe Clean Air Act and its amendments. Judging solely bythese data, would you say that Clean Air Act legislationhas been a success or a failure for U.S. citizens? Why?Critics of command-and-control policy often argue that regulationsare costly to business and industry, yet cost-benefitanalyses (p. 94) repeatedly show that regulations bring citizensmore benefits than costs, overall. Each year the U.S. Officeof Management and Budget assesses costs and benefits ofmajor federal regulations of administrative agencies. Resultsfrom the most recent report, covering the decade from 2003to 2013, are presented in the table (shown are averages fromranges of estimates). Subtract costs from benefits, and enterthese values for each agency in the third column. Divide benefitsby costs, and enter these values in the fourth column. Which agency’s regulations have the greatest excess ofbenefits over costs? Which agency’s regulations have thegreatest ratio of benefits to costs?
- Break-Even The total revenue function for Frenchdoor refrigerators is given by R = 550x dollars, andthe total cost function for this same product is givenby C = 10,000 + 30x + x2, where C is measured indollars. For both functions, the input x is the numberof refrigerators produced and sold.a. Form the profit function for the refrigerators fromthe two given functions. b. What is the profit when 18 refrigerators areproduced and sold?c. What is the profit when 32 refrigerators areproduced and sold?d. How many refrigerators must be sold to breakeven on this product?Suppose that you are the manager of a studio cafe, and you are planning to invest on a new camera and a coffee maker designed to increase the productivity of your employees and output (services) produced. Your analyst provided you the following information: Complete the table below. Current Situation Projected Sales and Profit Incremental Revenues and Costs Total Revenue Php1,500,000 Php1,800,000 Variable Cost 575,000 425,000 Direct Fixed Costs 625,000 700,000 Indirect Fixed Costs 100,000 100,000 Profit Should the new camera and coffee maker be purchased? Explain your answer based on the incremental analysis.Why CRS - Constant Returns on Scale would generate (1) No profit-maximizingproduction plan; the only nontrivial production plan involves zero profits. (2) Even when aprofit-maximizing plan exists, it is not unique?