Linear Programming Example 2 Alternate Optimal Solutions

The Problem An electronics company can manufacture three styles of 30-inch televisions: –Standard (.2 hrs in production,.1 hr assembly,.05 hours inspection – profit $60) –Flat Screen (.2 hrs in production,.3 hr assembly,.075 hours insepction – profit $90) –Plasma (.4 hrs in production,.4 hr assembly,.15 hours inspection – profit $100) Weekly Time Allocation Production 600 man-hours Assembly 480 man-hours Inspection 160 man-hours

Mathematical Model Decision Variables: X 1 = # Standard TV’s produced weekly X 2 = # Flat Screen TV’s produced weekly X 3 = # Plasma TV’s produced weekly Objective Max Total Weekly Profit MAX 60X X X 3 S.t. constraints Production:.2 X X X 3 ≤ 600 Assembly:.1 X X X 3 ≤ 480 Inspection:.05X X X 3 ≤ 160 Non-negativity: All X’s ≥ 0 Amount Used Amount available

=SUMPRODUCT($C$4:$E$4,C6:E6) Drag down

Optimal Weekly Production Schedule 1600 Standard /3 Flat 0 Plasma Work in Progress Profit =

Indicates alternate optimal solutions

Alternate Optimal Solutions An optimal solution that produces as many standard TV’s as possible. –Add a constraint that cell F6 must = –Then set objective function to MAX X 1 (cell C4) An optimal solution that produces as few standard TV’s as possible. –Add a constraint that cell F6 must = –Then set objective function to MIN X 1 (cell C4) An optimal solution that produces exactly twice the number of standard TV’s as flat screen TV’s. –Add a constraint X 1 = 2X 2.

Maximum Standard TV’s MAX C4 Objective Function = Optimal Weekly Production Schedule 2600 Standard 400 Flat 0 Plasma

Minimum Standard TV’s Objective Function = MIN C4 Optimal Weekly Production Schedule 1600 Standard /3 Flat 0 Plasma

Standard TV’s = 2* Flat Screen TV’s Optimal Weekly Production Schedule Standard Flat 0 Plasma Max Profit Standard = 2*(Flat Screen)

Review Recognizing Alternate Optimal Solutions How to Generate Alternate Optimal Solutions that: –Maximizes a decision variable –Minimizes a decision variable –Establishes so relationship between the variables