Quantitative Methods

Topics: Optimization, Profit maximization, Alternator Pages: 2 (298 words) Published: February 12, 2012
Statistics and Quantitative Methods
ASSIGNMENT: 2

PREPARED FOR:
CHOWDHURY

PREPARED BY:

VALLEY STATE UNIVERSITY
DATE:

13. The Electrotech Corporation manufactures two industrial-sized electrical devices: generators and alternators. Both of these products require wiring and testing during the assembly process. Each generator requires 2 hours of wiring and 1 hour of testing and can be sold for a \$250 profit. Each alternator requires 3 hours of wiring and 2 hours of testing and can be sold for a \$150 profit. There are 260 hours of wiring time and 140 hours of testing time available in the next production period and electrotech wants to maximize profit. (A) Formulate an LP model for this problem.

Decision Variable
X1 = Generator
X2 = Alternator
Obj. = Maximum Profit
X1| X2| Time| Activity|
2| 3| 260| Wiring|
1| 2| 140| Testing|

Max. Profit = 250X1 + 150X2
Subject to: 2x1 + 3x2 < 260
X1 + 2x2 < 140
X,y > 0

2x1 = 3x2 < 260
X1 =0x2 = 0
2(0) = 3x2 = 2602x1 = 3(0) =260
3x2 = 260 2x1 = 260
X2 = 86.7 x1 = 130

X1 + 2x2 = 140
X1 = 0x2 =0
2x2 = 140x1 = 2(0) 140
X2 = 70 x1 = 140

250x1 + 150x2 = Profit
Profit – 250x1 = 150x2
150x2 = Profit -250
150 150 150
X2 = profit/150 – 5/3 Rise/Run

(B) Sketch the feasible region for this problem.
See Attachment

(C) Determine the optimal solution to this problem using level curves. The optimal solution to this problem using level curves is 130.00 Total Profit \$32,500.00 or 41,175.00
See Attachment
In order for the Electrotech Corporation to maximize their profit they will have to produce 130 Generators 0 alternators for a maximum profit of 32,500. Any deviation from this will lower the company’s profit.