4 A company has contracted to sell certain quantities of a particular product ov

Question

4 A company has contracted to sell certain quantities of a particular product over the next four months. Because of variations in the size of the labour force, the production capacity and costs vary from month to month. Storage costs are incurred on any item carried over to a later month. (If the item is sold in the same month as production, no storage cost is incurred.) These costs are summarized below Month Contracted Production Production Storage Cost Sales 60 70 90 70 Capacity 90 60 80 100 Cost per Unit 70 72 70 65 per Unit 2 4 Formulate, but do not solve, the linear programming model to minimize costs

Explanation / Answer

Steps for Formulating using linear programming to minimize the cost:

Step 1:

Problem: Minimize the cost

Step 2:

Decision Variables:

Production cost + Storage Cost for all 4 months

Step 3:

Objective Function for the problem statement:

Minimize:

Production cost of month 1 + Storage cost of month 1 +

Production cost of month 2 + Storage cost of month 2 +

Production cost of month 3 + Storage cost of month 3 +

Production cost of month 4 + Storage cost of month 4

Minimize: 70P+2S+72P+1S+70P+1S+65P+3S

Step 4:

Constraints:

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