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## Fodak must schedule its production of digital camera

1. Fodak must schedule its production of digital camera memory card for the first fourmonths of the year. Memory card demand (in 1,000s of rolls) in January, February, Marchand April is expected to be 300, 500, 650 and 400, respectively. Fodak’s productioncapacity is 500 thousand memory cards per month. Business is highly competitive, soFodak cannot afford to lose sales or keep its customers waiting. Meeting month i ‘sdemand with month i +1’s production is unacceptable.Memory cards produced in month i can be used to meet demand in month i or can be heldin inventory to meet demand in month i +1 or month i +2 (but not later due to variousreasons). There are no units in inventory at the start of January.The production and delivery cost per thousand units will be \$500 in January andFebruary. This cost will increase to \$600 in March and April due to a new labor contract.Any memory cards put in inventory requires additional transport costing \$100 perthousand units. It costs \$50 per thousand units to hold memory cards in inventory fromone month to the next.a. Draw the network representation of this production & inventory application. Hint:Consider using a transshipment network (which you learned previously in thisclass) where transshipment nodes are each monthâs ending-inventory!To save time: Draw manually. Insert image/picture of your work on next page.b. Formulate and solve this problem to find the production and inventory quantities foreach of the 4 months so you can minimize total cost.c. Show formulation:d.What is the optimal Z and optimal solution?2. A large company may satisfy its fuel-oil requirements either by one annual contract ora series of separate monthly contracts throughout the winter. The cost for the annualcontract is \$0.80 per gallon. The cost for the monthly contract would depend onavailability of fuel during the year. With a monthly contract, if the year has ânormalâsupply of fuel-oil, the cost per gallon will average\$0.75 per gallon. But if the year hasâscarceâ supply, the price will average \$0.95 per gallon.The company will use 100,000 gallons during the year, and the manager estimates a 1/10chance (0.1 probability) of a scarce year.The manager may spend \$500 to obtain a professional economic forecast of whether theyear will be a normal or scarce one. Data on previous forecasts and actual occurrences forthe past 20 years is shown:Actual ResultsActual Normal (AN)Actual Scarce (AS)TotalForecast ResultsNormal (FN)Scarce (FS)15302155Total18220Construct a decision tree for this problem. Populate all branches with labels andprobability values. Include dollar amounts where appropriate. Then solve.To save time: Draw manually. Insert image/picture of your work on next page.Should the manager purchase the forecast?___ Yes___ NoWhat is the expected cost of Annual Contract? \$_________________What is the expected cost of Monthly Contract? \$________________

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