A production manager must plan the operations for the next week, which will be devoted to products P1, P2, P3, P4 and P5. There are four production workshops and the manager must respect the following constraints:

We cannot exceed the time available for the workshops.

It is necessary to produce at least as many units of P1 as of P2

A large order forces to manufacture at least 15 units of P4.

The total number of parts P3, P4 and P5 must not exceed the total number of parts P1 and P2.Les disponibilits sont de 250h, 144h, 160h et 175h pour les ateliers 1, 2, 3 4, respectivement. Le tableau suivant donne des informations pertinentes sur le profit unitaire des pices et le temps de production unitaire dans chaque atelier.

Workshop	P1	P2	P3	P4	P5
1	2h	6h	2h	2h	4h
2	1h	1h	1h	3h	1h
3	2h	2h	4h	4h	2h
4	3h	3h	11h	1h	2h
Profit $/unite	420	610	380	550	180

h: hours

a. Construct a linear model to determine the optimal production plan.

b. Solve the model using the Excel solver.