A manufacturer of an industrial product has to meet the following shipping sched

Question

A manufacturer of an industrial product has to meet the following shipping scheduel:

Month: Januar          Requierd shipment(units): 10,000

Month: February       Required shipment(units): 40,000

Month: March            Required shipment(units): 20,000

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

The company only uses storage when needed, to determine the monthly bill they multiply the number of units stored on the last day of the month by $3.

The company has 0 inventory in January and would like to have 0 at the end of march.

Formulate a mathematical model to assist in minimizing the sum of the production and storage cost for the 3-month persio?

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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