Consider the above question.

(a) Determine the optimality condition for / that will keep the optimum unchanged.

(b) Determine the optimality ranges for and , assuming that the other coefficient is kept constant at its present value.

(c) If the unit revenues and are changed simultaneously to $5 and $4, respectively, determine the new optimum solution.

(d) If the changes in (c) are made one at a time, what can be said about the optimum solution?

99. A company produces two products, A and B. The unit revenues are $2 and $3, respectively. Two raw materials, M1 and M2, used in the manufacture of the two products have daily availabilities of 8 and 18 units, respectively. One unit of A uses 2 units of M1 and 3 units of M2, and 1 unit of B uses 2 units of M1 and 6 units of M2. (a) Determine the dual prices of M1 and M2 and their feasibility ranges. (b) Suppose that 2 additional units of M1 can be acquired at the cost of 25 cents per unit. Would you recommend the additional purchase? (c) What is the most the company should pay per unit of M2? (d) If M2 availability is increased by 3 units, determine the associated optimum revenue