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ALY-6050 MOD 5 – Lab 1
(i) Linear Algebraic Modeling of LP Problems
(ii) R & Excel Solutions of LP Formulations

In this lab, we will first formulate a given linear programming problem using linear algebra. Furthermore, we will
obtain solutions by using both Excel and R.

Matrix Forms:

(i) Maximization Problems: (ii) Minimization Problems:
Maximize = Minimize =
Subject to: ≤ Subject to: ≥



Problem:
Suppose that a manufacturer makes 3 products. Let , , and denote the number of units of each type
respectiuvely. The model is described by the following formulation:
= + +
:
Constraint 1: + + ≤
Constraint 2: 3 + + ≤
Constraint 3: ≤ 0.4( + + ) → . − . − . ≤
Constraint 4: ≥ 250 → − ≤ − → ∶ + − ≤ −
Constraint 5: ≥ 0 → − ≤ → − + + ≤
Constraint 6: ≥ 0 → − ≤ → − + ≤


Therefore, the decision variables vector , the objective vector , the constraints’ matrix , and the vector of
the constraints’ right-hand sides are given by:


= ') , = '203040) , = ⎣⎢⎢
⎢⎢⎡ 130.6 15−0.4 18−0.40−10 00−1 −100 ⎦⎥⎥
⎥⎥⎤ , = ⎣⎢⎢
⎢⎢⎡ 100050000 −25000 ⎦⎥⎥
⎥⎥⎤


Task:
1. Formulate the above LP problem in Excel by using linear algebra and solve it by using the Solver.