HW3 Solutions

# HW3 Solutions - OSCM 230 Homework#3 HOMEWORK#3(SOLUTIONS...

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OSCM 230 Homework #3 H O M E W O R K #3(S O L U T I O N S ) L I N E A R P R O G R A M M I N G ( L P ) F O R M U L A T I O N 1. The problem is investing in the four securities so as to achieve maximum total return.  Define: TB CS MM MB = = = = amount to invest in Treasury Bonds amount to invest in Common Stock amount to invest in Money Market fund amount to invest in Municipal Bonds The formulation is then: Max  0.06 TB +0.12 CS +0.08 MM +0.08 MB   maximize expected return s.t. TB + MM +CS +MB =10 (fund invested) TB + MM   3  (at least 0.3  ×  10 in TB and MM) CS +MB   4   (at least 0.4  ×  10 in TB and MM)         TB   7    (upper bounds on each investment)          CS   2    (upper bounds on each investment)             MM   5    (upper bounds on each investment)         MB   4   (upper bounds on each investment) TB, MM, CS, MB   0  non-negativity   2.  This is a production model in which customer orders are allocated to one of three work centers (servers).    Let the decision variables be:  S 1w  = Web pages, Server 1 S 2w  = Web pages, Server 2 S 1d  = Database Queries, Server 1 S 2d  = Database Queries, Server 2 S 1e  = eCommerce, Server 1 S 2e  = eCommerve, Server 2 S 3w  = Web pages, Server 3 S 3d  = Database Queries, Server 3 S 3e  = eCommerce, Server 3

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OSCM 230 Homework #3 Problem Formulation: 1 1 1 2 2 2 3 3 3 1 2 3 1 3 1 2 1 1 1 2 2 3 3 2 3 1 1 1 2 2 2 3 3 3 : . 310 40 120 2.5 2 230 5 360 160 0 0 , , , , , , , , 0 w d e w d e w d e w w w e e d d w d e w e w d d e w d e w d e w d e Max S S S S S S S S S st S S S S S S S S S S S S S S S S S S S S S S S S S + + + + + + + + + + + + + + + + = = 3   This is a production model. The objective is to find an optimal mix of product models, allocated  among three production facilities, maximizing profit. Decision Variables:
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HW3 Solutions - OSCM 230 Homework#3 HOMEWORK#3(SOLUTIONS...

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