Question Instructions: Complete all problems. You can use either S

Instructions: Complete all problems. You can use either Solver, Lindo or excel to resolve problems. Be sure to indicate all variables and explain all models. All work must be done individually. You must turn in the template with answers incorporated. The work should also be contained within the worksheets of the template or you can submit a word document that illustrates your work. In each worksheet or word document you must:

Ø Identify / define the variables that are used in your model

Ø List any assumptions

Ø Highlight the answers and include the answers on the front (answer sheet) of the template

1. (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, it can sell 175 X1 0.75 12-packs of Classic Cola each week there. Moreover, if this company spends x2 dollars on promotion of Diet Cola in a particular western city, it can sell 150X2 0.75 12-packs of Diet Cola each week there. Each 12-pack of Classic Cola sells for $4.00 and costs $01.20 to produce and ship to customers in this western city. Each 12-pack of Diet Cola sells for $3.50 and costs $1.00 to produce and ship to customers in this western city. A total of $20,000 is available for promotion each week in this city. The soda producer seeks to maximize its weekly profit. Formulate and solve an appropriate optimization model to help this soda producer identify the best promotional strategies for its two products.

2. (20 points) Periodic preventive maintenance is carried out on aircraft engines, where an important component must be replaced. The number of aircraft scheduled for such maintenance 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 a used component may be replaced with a new or an overhauled component. The overhauling of used components may be done in a local repair facility, where they will be ready for use at the beginning of next month, or they may be sent to a central repair shop where a delay of 2 months (as such maintenance can occur in the third month) is expected. The repair cost in the local 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 $1.50 per 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 satisfying the demand for the component over the next 6 months. Also consider that the planning occurs within the first month. So all parts are ordered in the first month to satisfy maintenance requirements

3. (30 Pts) At the beginning of each day, a patient in a hospital is classified into one of three conditions; good, fair, or critical. At the beginning of the next day, the patient will either continue to be in the hospital and be in good, fair or critical condition or the patient will be discharged in one of three conditions: improved, unimproved or dead. The transition probabilities for these situations are as follows:

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