A customer requires during the next 4 months, respectively, 50, 65, 100, and 70 units of a commodity, and no backlogging is allowed (that is, the customer’s requirements must be met on time). Production costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit on hand at the end of month 4 could be sold for $6 (so that is a negative cost). Determine how much to produce each month to minimize the net cost incurred in meeting the demands for the next 4 months.

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Answer:

Check the explanation

Explanation:

Assumptions:

No inventory at beginning of month

Unlimited capacity

Other costs in production were ignored

Formulate the required Linear Problem:

[tex]X_{t}[/tex] is the number of commodities produced each month during month [tex]t[/tex]

[tex]i_{t}[/tex] is it is the number of commodities on hand at the end of month [tex]t[/tex]

Where, [tex]t[/tex] = 1,2,3,4 for each month in the problem

Thus, the total cost can be obtained in the attached images below

Ver imagen temmydbrain
Ver imagen temmydbrain