Q1. Our manufacturing plant produces bookshelves, couches, and worktables.
We have 400 hours of labor that are available to us each week, and 1000
units of lumber as raw materials. Each bookshelf produced yields a profit of
$6, consumes 12 hours of labor, and 40 units of lumber. Each couch yields a
profit of $5, consumes 14 hours of labor, and 22 units of lumber. Each
worktables yields a profit of $8, consumes 16 hours of labor, and 60 units of
lumber. Write a linear program to determine how many bookshelves,
couches, and worktables should be produced to maximize profits, subject to
labor and lumber restrictions. Write a linear programming model for the
problem. (Note: Make sure that you first define the decision variables, then
the objective
Q2. Consider the following LP:
2x₁+3x₂≤6
X₁, X₂20
max 2x₁-5x₂
s.t.3x₁ +8x₂≤12
(a) Compute all basic solutions and state which variables are basic and nonbasic. Indicate which
points are basic feasible solutions.
(b) Plot the feasible region.
(c) Identify the basic solutions of (a) in the graph of (b).
(d) Solve the LP with the Simplex Algorithm.
(e) Identify the basic feasible solutions computed during the Simplex Algorithm of part (d) within
the graph of part (b).