FINAL EXAM- A soda producer makes and sells two products, Classic Cola and Diet Cola.

Instructions: Complete all problems. You can use either Solver, Lindo or excel to resolveproblems. Be sure to indicate all variables and explain all models. All work mustbe done individually. You must turn in the template with answers incorporated.The work should also be contained within the worksheets of the template or youcan submit a word document that illustrates your work. In each worksheet or worddocument you must:Identify / define the variables that are used in your modelList any assumptionsHighlight the answers and include the answers on the front (answer sheet) ofthe template1. (10 points) – A soda producer makes and sells two products, Classic Cola and Diet Cola.If this company spends x1 dollars on promotion of Classic Cola in a particular western city, itcan sell 175 X1 0.75 12-packs of Classic Cola each week there. Moreover, if this companyspends x2 dollars on promotion of Diet Cola in a particular western city, it can sell 150X20.75 12-packs of Diet Cola each week there. Each 12-pack of Classic Cola sells for $4.00and costs $01.20 to produce and ship to customers in this western city. Each 12-pack of DietCola sells for $3.50 and costs $1.00 to produce and ship to customers in this western city. Atotal of $20,000 is available for promotion each week in this city. The soda producer seeks tomaximize its weekly profit. Formulate and solve an appropriate optimization model to helpthis soda producer identify the best promotional strategies for its two products.2. (20 points) Periodic preventive maintenance is carried out on aircraft engines, where animportant component must be replaced. The number of aircraft scheduled for suchmaintenance over the next 6 months is estimated at 200,180, 300,198,230, and 290,respectively. All maintenance work is done in the month that parts are available, where aused component may be replaced with a new or an overhauled component. The overhaulingof used components may be done in a local repair facility, where they will be ready for use atthe beginning of next month, or they may be sent to a central repair shop where a delay of 2months (as such maintenance can occur in the third month) is expected. The repair cost in thelocal shop is $120 per component. At the central facility, the cost is only $35 per component.An overhauled component used in a later month will incur an additional storage cost of $1.50per unit per month. New components may be purchased at $200 each in month 1, with a 5%price increase every 2 months. A new component is available immediately (no delay).Formulate a model to the problem and solve to determine the optimal schedule for satisfyingthe demand for the component over the next 6 months. Also consider that the planning occurswithin the first month. So all parts are ordered in the first month to satisfy maintenancerequirements13. (30 Pts) At the beginning of each day, a patient in a hospital is classified into one of threeconditions; good, fair, or critical. At the beginning of the next day, the patient will eithercontinue to be in the hospital and be in good, fair or critical condition or the patient will bedischarged in one of three conditions: improved, unimproved or dead. The transitionprobabilities for these situations are as follows:GoodFairCriticalGood.65.50.51GoodFairCriticalImproved.06.03.01Fair.20.30.25Critical.05.12.20Unimproved Dead.03.02.01.01.03.02For example, a patient who begins the day in fair condition has a 12% chance of being incritical condition the next day and a 3% chance of being discharged the next day inimproved condition.a. Consider a patient who enters the hospital in good condition. On average, howmany days does this patient spend in the hospital?b. This morning, there were 500 patients in good condition, 300 in fair condition,and 200 patients in critical condition in the hospital. Tomorrow morning, thefollowing admissions will be made: 50 patients in good condition, 40 in faircondition and 30 patients in critical condition. On the basis of this, predicttomorrows hospital census (how many patients in good, critical and faircondition, total)?c. The hospitals daily admissions are as follows: 20 patients in good condition, 10patients in fair condition and 10 patients in critical condition. On average, howmany patients of each type would you expect to see in the hospital (think steadystate conditions)?d. What fraction of patients who enter the hospital in good condition, will leave inimproved condition?224. Steco, a steel wholesaler, leases regional warehouses for its operation on a monthly basis.Steco currently has a list of three potential warehouses that it can lease. The cost per monthto lease each warehouse is shown in table 1 below. There are four sales districts in Stecosoperation. The monthly demand (in truck load requirements) is indicated in table 1 as well asthe unit cost of sending a truck from a warehouse to a given district. Steco wants to knowwhich warehouses to lease and how many trucks to send from each warehouse to eachdistrict that will minimize overall cost. Keep in mind that every warehouse does not have tobe used. Formulate an LP program and solve this problem. (10 pts)Table 1MonthlyCapacityMonthlyCost per truck from warehouse to Sales District (number of truck LeasingSales Districtsloads)CostWAREHOUSEABC1$170$150$1002$40$195$2403$70$100$1404$160$10$60MonthlyDemand (truckloads)1009011060200250300$7,750$4,000$5,5005. Newcors steel mill has received an order for 25 tons of steel. The steel must be 5% carbonand 5% molybdenum by weight. The steel is manufactured by combining three types of metals;steel ingots, scrap steel and alloys. Steel ingots can only be purchased in lot sizes of 1 at thespecified weights given in the table below. The ingot can be cut to the desired amount needed inthe process. The weight, cost per ton and chemical contents of each ingot is:INGOTCARBON%1WEIGHTMOLYBDENUM%COST PER TON5 tons$3505323 tons$3304334 tons$31054346 tons$28034Unlimited amounts of alloys and scrap steel can be purchased. Scrap steel cost $100 per tonand contains 3% carbon and 9% molybdenum. The cost per ton and chemical make up of thealloys is:ALLOYMOLYBDENUM%1$5002$4503$400COST PER TONCARBON%867768Determine the appropriate mixture of the steel components to minimize the cost of fulfillingthe requirements. 20 pts