A firm uses three raw materials (A, B, and C) to produce two final goods (P1 and P2). The number of units of the raw materials needed to produce one unit of P1 and P2 are summarized in the following production table, which also contains the available units of A, B, and C ('Capacities"): Product 1 Product 2 Capacities Raw Material A 10 5 600 Raw Material B 7 7 490 Raw Material C 5,5 14 770 The profit per unit of P1 is 70 Euro, the profit per unit of P2 is 50 Euro. The firm aims to maximize its total profits. a) Please formulate a linear optimization model. (9P) b) Please solve this model graphically. Highlight the feasible area, draw the target function and find the optimal solution. (10P) c) The firm receives an offer from a supplier to buy additional units of raw material C. Should the firm accept the offer? Please explain your answer. (3P)