PLEASE YOU HAVE TO THINK BEFORE TO ANSWER THIS QUESTION AND I KNOW IT HAS BEEN ALREADY SOLVED BY OTHER EXPERTS BUT THERE IS A SMALL DIFFERENCE WHEN IT COMES TO THIS STATEMENT "At the beginning of month 1 there are 20 units in stock "

OPERATIONS RESEARCH

A company produces a certain product and has the capacity to produce 100 units per month in regular time, and an additional 15 units per month in overtime. The production cost of the product varies by month due to changes in the material costs over time. The quantities of the product to be delivered over the next six months have already been set. The delivery requirements and production costs are given in the following table:

It is possible that the units produced in a month exceeds the delivery requirement. In such a case, the unsold units are then carried in stock to the following month. The cost of carrying an unsold unit in stock is 12 Usd per unit per month.

At the beginning of month 1 there are 20 units in stock and the company does not want to have any unsold units at the end of month 6. The company must determine the number of units of the product to produce in regular time and in overtime each month to meet the delivery requirement at minimum cost.

QUESTIONS

(a) Define the decision variables that will be needed to formulate a linear programming (LP) model for this problem.

(b) Formulate the Linear Programming (LP) model that represents this problem.

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BE CAREFUL WITH THIS STATEMENT " At the beginning of month 1 there are 20 units in stock "

Month Quantities to be delivered (units) Production cost per unit in regular time (Usd) Production cost per unit in overtime (Usd) 1 95 180 210 2 85 180 210 3 110 192 4 115 192 222 5 6 90 100 186 192 216 222 222