Olympic Bike is introducing two new lightweight bicycle frames, the Deluxe and the Professional, to be made from special aluminum and steel alloys. The anticipated unit profits are $15 for the Deluxe and $17 for the Professional. The number of pounds of each alloy needed per frame is summarized in the table. A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy weekly.

Aluminum Alloy Steel Alloy

Deluxe 1 2/3

Professional 2 1

1. Develop and solve LP model to decide how many Deluxe and Professional frames should Olympic produce each week to maximize the total profit.
2. What are the dual values (shadow prices)? Interpret each.
3. Which constraints show extra (unused) alloy? How much?