XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.Determine the capacity constraint for patching operation.Let x1 = Number of soft panels to be made,x2 = Number of hardwood panels to be made,x3 = Number of tropical panel to be made,and x4 = Number of aircraft panels to be made.

A)X₁ ≥ 100
B)0.6X₁ + 1X₂ + 2.0X₃ + 2.5X₄ ≤ 2,500
C)X₄ ≥ 250
D)X₁ + 2X₂ + 3X₃ + 4X₄ ≤ 4,000

Question

XYZ manufactures four types of plywood panels.Each product must go through the following operations: patching,grading,gluing,and baking.The time requirements for each panel,the capacity available,the minimum production requirements,and the profit contributions per panel are tabled here.Determine the capacity constraint for patching operation.Let x1 = Number of soft panels to be made,x2 = Number of hardwood panels to be made,x3 = Number of tropical panel to be made,and x4 = Number of aircraft panels to be made.

A)X₁ ≥ 100 
B)0.6X₁ + 1X₂ + 2.0X₃ + 2.5X₄ ≤ 2,500 
C)X₄ ≥ 250 
D)X₁ + 2X₂ + 3X₃ + 4X₄ ≤ 4,000

Quizplus · Accepted Answer

To determine the capacity constraint for patching operation, we need to look at the "Patching" row in the table.
The time requirement for patching is 0.6 minutes per soft panel and the available capacity is 2,500 minutes. Therefore, the constraint is:
0.6X₁ ≤ 2,500 
which simplifies to 
X₁ ≤ 4,166.67
However, we also have a minimum production requirement of X₁ ≥ 100 soft panels. Therefore, the capacity constraint for patching is:
100 ≤ X₁ ≤ 4,166.67
The only choice that represents this capacity constraint is B) 0.6X₁ + 1X₂ + 2.0X₃ + 2.5X₄ ≤ 2,500.

XYZ Manufactures Four Types of Plywood Panels