{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

IEOR162_Midterm1_sol

# IEOR162_Midterm1_sol - IEOR 162 Fall 2011 Suggested...

This preview shows pages 1–2. Sign up to view the full content.

IEOR 162, Fall 2011 Suggested Solution to Midterm 1 1. Let x i = production quantity of product i , i = 1 , 2. To produce x 1 units of product 1, we need x 1 units of component 1 and 2 x 1 units of component 2. To produce x 2 units of product 2, we need 2 x 2 units of component 1 and 3 x 2 units of component 2. Therefore, in total we need x 1 + 2 x 2 units of component 1 and 2 x 1 + 3 x 2 units of component 2. This requires 50( x 1 + 2 x 2 ) + 10(2 x 1 + 3 x 2 ) = 70 x 1 + 130 x 2 dollars. To maximize the sales revenue (not profit), we formulate the problem as min 120 x 1 + 200 x 2 s.t. 70 x 1 + 130 x 2 1000 (budget constraint) x 1 + 2 x 2 10 (supply limitation of component 1) x i 0 i = 1 , 2 . 2. (a) To remove x 3 , note that the third constraint must be binding at the optimal solution: If it is not, we may decrease x 3 and improve our solution. Therefore, the third constraint can be rewritten as - x 1 + x 2 - x 3 = 0, or x 3 = - x 1 + x 2 . Then we may remove the third constraint and replace x 3 in the objective function by - x 1 + x 2 . This results in the following equivalent LP

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}