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Linear programming problem in Introduction to Operating research

Yogurt company produces three types of yogurt, S1, S2 and S3. The production manager of the company needs assistant to make a production plan for the second quarter of 2018 (May, June, July and August). In the following table you can find the production cost for every item and the output per day considering that only one product is in production per day. 22 days are used in each month to product. We can arrange the total day each month to produce the three items like we like, for example we want 10 days to product S1(10*5.000=50.000), 5 days to product S2(5*4.500=22.500) og 2 days to product S3(2*5.500=11.000). Notice that in July it is only possible to produce for 11 days because of summer vacations.

Production S1 S2 S3 Production cost (cents/piece) 0,44 0,27 0,38 Output (piecec per day) 5.000 4.5005.500

Wholesale price of the items are 1 dollar for S1, 0,83 dollar for S2 and 0,96 for S3. The most possible amount that we can sell of each item each month is given in the following table:

June July August Mos demand (piece)May 43.000 42.000 64.000 53.000 S1 45.000 54.000 65.000 72.000 S2 54.000 67.000 78.000 82.000 S3

Formulate a linear programming model that can be used to determine the production with the goal to maximize the profit. Explain premises, variables, objective function and constrains.

Linear program includes

*decision variables

*objective functions

*constrains

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