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Fodak must schedule its production of camera film for the first four months of the year. Film demand (in 1,000s of rolls) in January, February, March and April is expected to be 300, 500, 650 and 400, respectively. Fodak's production capacity is 500 thousand rolls of film per month. The film business is highly competitive, so Fodak cannot afford to lose sales or keep its customers waiting. Meeting month i 's demand with month i +1's production is unacceptable.
Film produced in month i can be used to meet demand in month i or can be held in inventory to meet demand in month i +1 or month i +2 (but not later due to the film's limited shelflife). There is no film in inventory at the start of January.
The film's production and delivery cost per thousand rolls will be $500 in January and February. This cost will increase to $600 in March and April due to a new labor contract. Any film put in inventory requires additional transport costing $100 per thousand rolls. It costs $50 per thousand rolls to hold film in inventory from one month to the next.
a.
Modeling this problem as a transshipment problem, draw the network representation.
b.
Formulate and solve this problem as a linear program.
Unit Selling Price
The amount of money charged to the customer for a single unit of product or service.
Contribution Margin
The difference between sales revenue and variable costs, representing the amount that contributes to covering fixed costs and generating profit.
Contribution
The portion of sales revenue that exceeds variable costs, contributing towards covering fixed costs and generating profit.
Machine Hour
A measurement of production time, quantifying the number of hours a machine is in operation during a given period.
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