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Juiceco manufactures two products: premium orange juice and regular orange juice. Both products are made by combining two types of oranges: grade 6...
4.Juiceco manufactures two products: premium orange juice and regular orange juice. Both products are made by combining two types of oranges: grade 6 and grade 3. The oranges in premium juice must have an average grade of at least 5, those in regular juice, must have an average grade of at least 4. During each of the next two months, Juiceco can sell up to 1000 gallons of premium juice and up to 2000 gallons of regular juice. Premium juice sells for $1 per gallon and regular juice sells for $.80 per gallon. At the beginning of month 1 Juiceco has 3000 gallons of grade 6 oranges and 2000 gallons of grade 3 oranges. At the beginning of month 2, Juiceco may purchase additional grade 3 oranges for $.40 per gallon and additional grade 6 oranges for $.60 per gallon. Juice spoils at the end of the month, so it makes no sense to make extra juice during month 1 in hopes of using it to meet month 2 demand. However, oranges left at the end of month 1 may be used to produce juice for month 2. At the end of the month a holding cost of $.05 is assessed against each gallon of leftover grade 3 oranges and $.10 against each gallon of leftover grade 6 oranges. In addition to the cost of oranges, it cost $.10 to produce each gallon of (regular or premium) juice. Determine the mixture of oranges that maximizes profit (revenue - cost) (15 pts)5.You are the General Manager of a US owned plant located in Northern Mexico. The firm manufactures semiconductors and uses temporary employees from the local area to fulfill production labor requirements. Each quarter employees are hired and released depending upon production requirements and needs. The firm has a maximum storage capacity of 1,000,000 semiconductors. Agreements with the Mexican Government require that at least 325 workers must be on the payroll each quarter. There are currently 375 employees on the payroll and 120,000 semiconductors in storage. Sales forecast provided by the marketing department are estimated as follows for the upcoming year:PREDICTEDDAYS SALES FORECAST940,000Second62 1,215,000860,000430,000Inventory holding cost are $.25 per semiconductor per quarter. The holding cost applies to excess inventory after demand is fulfilled. Thus, assume inventory produced in the quarter to fulfill demand in that quarter is not subjected to holding cost. (15 Points)Wheat sells for $30 per bushel, alfalfa sells for $200 per bushel, and beef sells for $300 per ton. Up to 1000 bushels of wheat and up to 1000 bushels of alfalfa can be sold, but demand for beef is unlimited. If an acre of land is devoted to raising wheat, alfalfa or beef, the yield and required labor are given below:CROPYIELD/ACRELABOR/ACRE30 hours20 hours50 hoursUp to 2000 hours of labor can be purchased at $15 per hour. Each acre devoted to beef requires 5 bushels of alfalfa. The LINDO output is attached and shows how to maximize profit. The variables are as follows:W = acres devoted to wheatAS = bushels of alfalfa soldA = acres devoted to alfalfaB = acres devoted to beefAB = bushels of alfalfa devoted to beefL = hours of labor purchasedAnswer the following questions and justify your answers from the Lindo solution provided on the next page (20 pts)a) How much must the price of a bushel of wheat increase before it becomes profitable to grow wheat?b) Old Macdonald is offered 2000 bushels of alfalfa at a cost of $150 per bushel. Should Old Macdonald accept this offer? What affect would this have on profit?c) What is the most Old Macdonald is willing to pay for an additional hour of labor?d) Old Macdonald is offered 25 additional acres of land at a cost of $60 per acre. Should Old Macdonald accept this offer? What affect would this have on profit?e) What would be the new solution if alfalfa sold for $20 per bushel?LINDO Output (Model):max 1500W + 200AS + 3000B -15LS.T.50W<=1000AS<= 1000AS + AB -100A = 0AB - 5B = 0W + B + A <= 200L <= 200030W + 50B - L + 20A <= 0Solution:OBJECTIVE FUNCTION VALUE275882.3REDUCED COST264.7058720.0000000.0000000.0000000.0000000.000000DUAL PRICES 0.000000188.235291 11.764706 -11.7647060.000000 43.82352858.8235281 RANGES IN WHICH THE BASIS IS UNCHANGED:OBJ COEFFICIENT RANGESALLOWABLEDECREASEINFINITY188.235291449.99990843.82352889.9999858999.998047RIGHTHAND SIDE RANGESALLOWABLE DECREASE1000.0000001000.0000008999.999023180.000000152.9411771799.9998781799.999878
