The production planning problem that we study here consists in determining

the launch of production in a given period with the number of units (or

of parts) to be produced. Suppose we have 6 weeks whose requests

clientele are 100, 200, 250, 225, 300 and 125 units for weeks 1 to 6,

respectively. The capacity of the weekly production is assumed to be infinite. The

production can be started on Monday morning and it must be stopped on Friday evening of

every week. The production launch each week costs $ 1000 * and

each unit manufactured costs $ 20, $ 25, $ 15, $ 10, $ 20 and $ 30, respectively for

weeks 1 to 6 **. It is possible to produce more than demand

Weekly and store surplus from week to week with storage cost

$ 2 per piece.

Give a mathematical optimization model that makes it possible to find a plan of

production in order to minimize the costs mentioned above.

* If the production is not launched within a week d, then the cost of launching the

production is zero.

** Example: if we decide to produce 100 units in week 1, it costs us:

$ 1000 + $ 20 * 100.

NB: CAN YOU PLEASE DO IT WITHOUT EXCEL, I NEED THE ANSWER WRITE BY HAND.