I need help with my homework this is only for practice to give us an idea of what our final will be like ASAP my exam is on friday

Consider an industry with 3 firms selling homogeneous products. The cost function, the same for each firm i=1,2,3, is C_i(q i)=50q_i+300 Demand for the product is P=170-Q.| 2. Assume that firms 1 and 3 merge. The merged firm is called firm m, while firm 2 is the non-merging firm. The resulting market is a Cournot duopoly. The merger allows the newly formed firm, firm m, to save on fixed costs. After the merger, the cost function is C_m(q m)=50q_m+400 The non-merging firm, firm 2, still has the same cost function as before: C_2(q 2)=50q_2+300 (a) Derive the reaction functions for each firm. (1 point) (b) Derive the equilibrium quantities, price and profits. (1 point) (c) Is the merger profitable? Compute and explain. (1 point)