Exhibit 3.1 The Following Questions Are Based on This Problem and Accompanying

Exhibit 3.1
The following questions are based on this problem and accompanying Excel windows.
Jones Furniture Company produces beds and desks for college students.The production process requires carpentry and varnishing.Each bed requires 6 hours of carpentry and 4 hour of varnishing.Each desk requires 4 hours of carpentry and 8 hours of varnishing.There are 36 hours of carpentry time and 40 hours of varnishing time available.Beds generate $30 of profit and desks generate $40 of profit.Demand for desks is limited,so at most 8 will be produced.
Let ^X₁ ^{= Number of Beds to produce} X₂ = Number of Desks to produce
The LP model for the problem is
MAX: ^{30 X}₁ ^{+ 40 X}₂
Subject to: ^{6 X}₁ ^{+ 4 X}₂ ^{≤ 36 carpentry)}
4 X₁ + 8 X₂ ≤ 40 varnishing)
X₂ ≤ 8 demand for desks)
X₁,X₂ ≥ 0

-You have been given the following linear programming model.
MAX: ^{8 X}₁ ^{+ 5 X}₂
Subject to: ^{3 X}₁ ^{+ 5 X}₂ ^{= 54}
11 X₁ + 10 X₂ ≤ 144 X₁ / X₂ ≥12
X₁,X₂ ≥ 0
This formulation:

A) can be solved without preprocessing using LP
B) cannot be solved using LP
C) requires that the third constraint be first converted to a linear form: X₁ - 12 X₂ ≤ 0
D) must be first converted to a minimization problem