2.) A company manufactures two types of products, A and B. The unit revenues are $2...

2.) A company manufactures two types of 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 4 and 6 units, respectively. One unit of A uses 1 unit of M1 and 1 unit of M2, and one unit of B uses 1 unit of M1 and 2 units of M2.

a) Formulate a linear programming model and obtain the optimal solution using the graphical method.

b) Recall that shadow/dual price is the change in the objective function for every unit change in the right hand side of the constraint. Find shadow/dual price for the first constraint in your model. Find also the range where this shadow price remains valid.

c) Repeat part (b) for the second constraint.

d) If M2 availability is increased by 2 units, determine the associated optimal revenue.

e) Suppose that 2 additional units of M2 can be acquired at the cost of 30 cents per unit. Would you recommend the additional purchase?

f) Let c1 and c2 be the prices of products A and B, respectively. Find the optimality range of the ratio c1/c2 that will keep the optimum solution unchanged at the pivot point (2, 2).

g) Ask solver to produce the sensitivity report and print it and turn in along with your homework

Expert Solution

keosha answered 11 months ago

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