Make sure to type the question number/letter clearly.Also, PLEASE use the notations provided for each question.

PLEASE HELP!!

Problem 1)

Consider the following LP problem:

x < 11 ; x + y = 15; y < 9

Questions:

a) Define each of the three (hard) constraints as goal (target) constraints. Use notations like d1p, d2n, ... for the deviation variables where p and n represent overachievement and underachievement, respectively (e.g., d3n would be the underachievement variable for constraint number 3 if such a variable is needed).

b.) Define the objective function of the goal programming model.

Problem 2)

Recall Ralph's diet problem where S and P denote the (main) decision variables representing the number of daily servings of steak and potatoes in the diet. Now rewrite the formulation as a goal programming model using the same notations as Problem 1 for deviation variable. Requested details as follows:

Questions:

a) Define all three (main) constraints of the problem by converting them into goal (target) constraints.

b)Assuming a maximum diet cost target of $35, write goal constraint for the total cost of the diet.

c) Define the objective function as the sum of deviation variables.

d) What approach would you suggest to solve this goal programming model? Just name the approach; no need to solve it.

Problem 3)

Consider a company produces three different types of products (represented by a, b, and c as the production amounts in tons). The company would like to maximize its total output in tons and minimize its total cost in dollars that are expressed as follows:

oMaximize a + b+ c

oMinimize 200a + 300b + 400c

Suppose we have a target tonnage of 10 tons and a target cost of 0 dollars. If you were to write or describe a goal programming model for the company:

Questions:

a) Define the goal constraint for each of the above goals (Hint: To start, consider the targets as equality goal constraints. For deviation variables, use the same notations as Problems 1 and 2.)

b)What deviation variable would you use to minimize for the tonnage maximization goal? For the cost minimization goal?

c)Define the objective function of the goal programming model for this problem using a weighted-sum approach, assuming that the tonnage goal is three times as important.