A manufacturer has to meet the following shipping schedule: In the month of JANU

Question

A manufacturer has to meet the following shipping schedule:

In the month of JANUARY, he is requried shipment units : 10,000

In the month of FEBRUARY, he is required shipment units: 40,000

In the month of MARCH, he is required shipment units: 20,000

Production capacity is 30,000 units and the production cost per unit is $10.

Because the company does not warehouse, storare company is utilized when needed, the bill gets determined by multiplying the number of units in storage on the last day of the month by $3.

The company start of with zero in january and would like to end with zero at the end of march.

Formulate a mathematical model to assist in minimzing the sum of the production and storage cost for the 3 month period.

Explanation / Answer

Let the number of units produced in Jan=x;Feb=y;Mar=z; Total Production Cost=(10*x+10*y+10*z) The units remaining after shipping the required goods as given will go to storage Hence the storage costs can be determined as : Jan=(x-10000)*3=3x-30000; In the next month y units are produced and combining the units from storage house, the required units are shipped. The remaining are sent to storage again. Feb=(x-10000+y-40000)*3=3x+3y-150000; Similarly March=(x+y+z-10000-40000-30000)*3=3x+3y+3z-210000 It is given that by the end of March no products should remain in the storage. Hence x+y+z=70000 becomes the constraint. Hence the Total Costs becomes = 19x+16y+13z-390000 which is to be MINIMIZED subject to the constraints (x+y+z=70000) and x

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