The corner points of the feasible region determined by the system of linear constraints are as shown below:
Answer each of the following:
(i) Let 𝑍 = 3𝑥−4𝑦 be the objective function. Find the maximum and minimum value of Z and also the corresponding points at which the maximum and minimum value occurs.
(ii) Let 𝑍=𝑝𝑥 + 𝑞𝑦, where 𝑝,𝑞>𝑜 be the objective function. Find the condition on 𝑝 and 𝑞 so that the maximum value of 𝑍 occurs at B(4,10)𝑎𝑛𝑑 C(6,8). Also mention the number of optimal solutions in this case.