# Maximizing profits and Optimal solutions for each problem stated.

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Quantitative Analysis for Management

Assignment 1

When solving the following problems kindly show all your work in details!

Question 1: Graphically solve the following problem, After identifying the Decision Variables, Objective Function and Constraints.

A clothing company makes short- sleeve and long- sleeve shirts.

Each long-sleeve shirt nets the company \$4 in profit and each short sleeve nets the company \$3.

Each shirt must be processed by two sewing machines—Machine I and Machine II.

Long-sleeve shirts require 3 minutes on Machine I and 1 minute on Machine II.
Short-sleeve shirts require 2 minutes on each machine.
Every day, Machine I is available for 10 hours and Machine II is available for 7 hours.

How many shirts of each type should the company produce each day so as to maximize profits?

Question 2: Graphically solve the following problem:

Minimize the cost= X+2Y

Subject to: X+3Y

X,Y

1. A) What is the optimal solution?
2. B) Change the right hand side of constraint 2 to 140 (instead of 160) and resolve the problem. What is the new optimal solution?

ccQuantitative Analysis for Management

Assignment 1

When solving the following problems kindly show all your work in details!

Question 1: Graphically solve the following problem, After identifying the Decision Variables, Objective Function and Constraints.

A clothing company makes short- sleeve and long- sleeve shirts.

Each long-sleeve shirt nets the company \$4 in profit and each short sleeve nets the company \$3.

Each shirt must be processed by two sewing machines—Machine I and Machine II.

Long-sleeve shirts require 3 minutes on Machine I and 1 minute on Machine II.
Short-sleeve shirts require 2 minutes on each machine.
Every day, Machine I is available for 10 hours and Machine II is available for 7 hours.

How many shirts of each type should the company produce each day so as to maximize profits?

Question 2: Graphically solve the following problem:

Minimize the cost= X+2Y

Subject to: X+3Y

X,Y

1. A) What is the optimal solution?
2. B) Change the right hand side of constraint 2 to 140 (instead of 160) and resolve the problem. What is the new optimal solution?

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