The PGR Corporation is planning to produce three different products. Letx1,x2, andx3 denote the number of units of the three respective products to be produced. The preliminary estimates of their potential profitability are as follows:For the first 10 units produced of Product 1, the unit profit would be $360. The unit profit would be only $30 for any additional units of Product 1. For the first 22 units produced ofProduct 2, the unit profit is estimated at $240. The unit profit would be $120 for each of the next 15 units and $90 for any additional units. For the first 5 units of Product 3, the unit profit would be $450. The unit profit would be $300 for each of the next 10 units and $180 for any additional units. Certain limitations on the use of needed resources impose the following constraints on the production of the three products:x1+x2+x3≤603x1+2x2≤200x1+2 x3≤70x1,x2,x3≥0 Please do the following
1. Plot the profit graph for each of the three products (10 points).
2. Formulate a separate programming model for this problem utilizing the 5-steps process discussed in class (20 points).
3. Solve this problem utilizing Excel solver and provide the appropriate recommendations and expected profits (20 points).
4. (Bonus question) Briefly discuss the implications of the solution of this problem under a sustainable operations approach. Specifically, discuss how these decisions would have the following impact (5bonus points):a) economical impact b) environmental impact) social impact