37. The New England Cheese Company produces two cheese spreads by blending mild cheddar cheese with extra sharp cheddar cheese. The cheese spreads are packaged in 12-ounce containers, which are then sold to distributors throughout the Northeast. The Regular blend contains 80% mild cheddar and 20% extra sharp, and the Zesty blend contains 60% mild cheddar and 40% extra sharp. This year, a local dairy cooperative offered to provide up to 8100 pounds of mild cheddar cheese for $1.20 per pound and up to 3000 pounds of extra sharp cheddar cheese for $1.40 per pound. The cost to blend and package the cheese spreads, excluding the cost of the cheese, is $0.20 per container. If each container of Regular is sold for $1.95 and each container of Zesty is sold for $2.20, how many containers of Regular and Zesty should New England Cheese produce?
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- PRICING SUITS AT SULLIVANS Sullivans is a retailer of upscale mens clothing. Suits cost Sullivans 320. The current price of suits to customers is 350. which leads to annual sales of 300 suits. The elasticity of the demand for mens suits is estimated to be 2.5 and assumed to be constant over the relevant price range. Each purchase of a suit leads to an average of 2.0 shirts and 1.5 ties being sold. Each shirt contributes 25 to profit, and each tie contributes 15 to profit. Determine a profit-maximizing price for suits. In the complementary-product pricing model in Example 7.3, we have assumed that the profit per unit from shirts and ties is given. Presumably this is because the prices of these products have already been set. Change the model so that the company must determine the prices of shirts and ties, as well the price of suits. Assume that the unit costs of shirts and ties are, respectively, 20 and 15. Continue to assume that, on average, 2.0 shirts and 1.5 ties are sold along with every suit (regardless of the prices of shirts and ties), but that shirts and ties have their own separate demand functions. These demands are for shirts and ties purchased separately from suit purchases. Assume constant elasticity demand functions for shirts and ties with parameters 288,500 and 1.7 (shirts), and 75,460 and 1.6 (ties). Assume the same unit cost and demand function for suits as in Example 7.3. a. How much should the company charge for suits, shirts, and ties to maximize the profit from all three products? b. The assumption that customers will always buy, on average, the same number of shirts and ties per suit purchase, regardless of the prices of shirts and ties, is not very realistic. How might you change this assumption, and change your model from part a accordingly, to make it more realistic?1. A distillery produces two types of alcohol for filling and distributing, the regular beer and the premium beer. A batch of regular costs $375 to manufacture and a container of the Premium beer costs $420. The manufacturer wishes to establish the weekly production plan that minimizes cost. Production of these products is limited to processing, testing and material. Each batch of regular beer requires 4 hours processing whereas each batch of premium requires 2 hours of processing. Further each batch of regular requires 4 hours of testing compared to 6 hours of testing for a batch of Super. A batch of regular and a batch of Super each require 1 litre of material. Processing and testing have a maximum of 100 and 180 hours available and the total material available is 40 litres. Because of an agreement, the sales of regular beer are limited to a weekly maximum of 20 batches and to honour an agreement with a loyal distributor, at least 10 batches of premium beer must be sold each week.…2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per P40,000 invested. The Diversified fund has a risk rating of 4 per P40,000 invested. For example, if P400,000 is invested in each of the two investment funds, Provident’s risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, Provident developed…
- As part of a campaign to promote its annual clearance sale, Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's television advertising budget is $111,000. Morning time costs $3000/min, afternoon time costs $1000/min, and evening (prime) time costs $12,000/min. Because of previous commitments, KAOS cannot offer Excelsior more than 6 min of prime time or more than a total of 25 min of advertising time over the 2 weeks in which the commercials are to be run. KAOS estimates that morning commercials are seen by 200,000 people, afternoon commercials are seen by 100,000 people, and evening commercials are seen by 600,000 people. How much morning, afternoon, and evening advertising time should Excelsior buy to maximize exposure of its commercials? morning min afternoon min evening minEastern Chemicals produces two types of lubricating fluids used in industrial manufacturing. Both products cost Eastern Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Eastern Chemicals’ management specified that at least 30 gallons of product 1 and at least 20 gallons of product 2 must be produced during the next two weeks. Management also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next two weeks. The current inventory of the perishable raw material is 80 pounds. Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next two weeks will spoil—hence, the management requirement that at least 80 pounds be used in the next two weeks. Furthermore, it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2…Eastern Chemicals produces two types of lubricating fluids used in industrial manufacturing. Both products cost Eastern Chemicals $1 per gallon to produce. Based on an analysis of current inventory levels and outstanding orders for the next month, Eastern Chemicals’ management specified that at least 30 gallons of product 1 and at least 20 gallons of product 2 must be produced during the next two weeks. Management also stated that an existing inventory of highly perishable raw material required in the production of both fluids must be used within the next two weeks. The current inventory of the perishable raw material is 80 pounds. Although more of this raw material can be ordered if necessary, any of the current inventory that is not used within the next two weeks will spoil—hence, the management requirement that at least 80 pounds be used in the next two weeks. Furthermore, it is known that product 1 requires 1 pound of this perishable raw material per gallon and product 2 requires 2…
- The manager of Jokitian Iron Works Company received an order to produce anumber of pipes which require the use of material A costing $3 and material Bcosting $8 per unit. For each pipe no more than 12 units of Material A and at least16 units of material B must be used. While each unit of A weighs 4 pounds andeach unit of B weighs 6 pounds, the final product must weigh exactly 120 pounds.a. Present the objective function.b. Present the constraint functions.c. Show and label the graph of the feasible solution.d. How many units of each raw material should be used in order to producethe ordered pipes most economically?e. What is the cost of each pipe?A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.c. If the replenishment lead time for wafers is three months, determine the reorderpoint based on the on-hand level of inventory of wafersA purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.b. What is the optimal value of the holding and setup costs for wafers when theoptimal source is used?
- A purchasing agent for a particular type of silicon wafer used in the production ofsemiconductors must decide among three sources. Source A will sell the siliconwafers for $2.50 per wafer, independently of the number of wafers ordered. Source Bwill sell the wafers for $2.40 each but will not consider an order for fewer than3,000 wafers, and Source C will sell the wafers for $2.30 each but will not acceptan order for fewer than 4,000 wafers. Assume an order setup cost of $100 and anannual requirement of 20,000 wafers. Assume a 20 percent annual interest rate forholding cost calculations.a. Which source should be used, and what is the size of the standing order?Markus, Inc., has harvested 400 tons of lumber from a pine forest located outside of Manchester, 200 tons from a forest near Seattle, and 150 tons from a forest outside of Portland. Japan has placed an order for 300 tons at a price of $1200 per ton, Taiwan needs 300 tons and will pay $1000 per ton, and Singapore wants 250 tons at $1000 per ton. It costs Markus, Inc. $500 to get each ton from the pine forest to the port in Manchester, $400 per ton to the port in Seattle, and $300 per ton to Portland. Assume that each pine forest only supplies its closest port. The following table provides the cost for shipping each ton by sea from these ports to the respective countries: ________________________________________________________________________ SHIPPING COST ($/TON) OF LUMBER BY SEA TO: FROM JAPAN TAIWAN SINGAPORE Manchester 250 250 200 Seattle 250 200 200 Portland…Ariel holds a $10,000 portfolio that consists of four stocks. Her investment in each stock, as well as each stock’s beta, is listed in the following table: Stock Investment Beta Standard Deviation Andalusian Limited (AL) $3,500 0.80 15.00% Kulatsu Motors Co. (KMC) $2,000 1.50 12.00% Western Gas & Electric Co. (WGC) $1,500 1.20 16.00% Makissi Corp. (MC) $3,000 0.50 22.50% Suppose all stocks in Ariel’s portfolio were equally weighted. Which of these stocks would contribute the least market risk to the portfolio? Makissi Corp. Andalusian Limited Western Gas & Electric Co. Kulatsu Motors Co. Suppose all stocks in the portfolio were equally weighted. Which of these stocks would have the least amount of standalone risk? Western Gas & Electric Co. Makissi Corp. Andalusian Limited Kulatsu Motors Co. If the risk-free rate is 4% and the market risk premium is 6%, what is Ariel’s…