Part of understanding linear programming is knowing how to d

Part of understanding linear programming is knowing how to do the algebra to identify the points where you are using all of both items to either maximize profit or minimize loss.

So, to give you additional practice with the algebra of linear programming, do the following:

Step 1: If your last name ends in A-H, do problem #1. If your last name ends in I-P, do problem #2. If your last name ends in Q-Z, do problem #3.

Problem 1 – Use your class notes and textbook to solve for X₁ and X₂:

2X₁ + 4X₂ = 80

3X₁ + 1X₂ = 60

Problem 2 – Use your class notes and textbook to solve for X₁ and X₂:

2X₁ + 4X₂ = 400

100X₁ + 50X₂ = 8000

Problem 3 – Use your class notes and textbook to solve for X₁ and X₂:

4X₁ + 6X₂ = 48

4X₁ + 2X₂ = 12

Step 2: Once you have determined the answers for X₁ and X₂ in each problem, count how many letters you have in your first and last name. The number of letters in your first name will equal the profit per item for X₁ and the number of letters in your last name will be the profit per item for X₂.

Then multiply the answer you came up with for X₁ by the number of letters in your first name, and then multiply the answer you came up with for X₂ by the number of letters in your last name.

Example: Both my first and last name are each 4 characters long. If X₁ is 10 and X₂ is 15, I would multiply (10*4) = $40 and (15*4) = $60.  So, your profit for X₁ would be $40 and your profit for X₂ would be $60, for a total profit of $100.

Step 3: Answer the following questions:

a. Based on your last name, which problem (1, 2, or 3) did you solve? (value: 10 points)

b. What answer did you get for X₁? (value: 20 points)

c. What answer did you get for X₂? (value: 20 points)

d. Based on the number of characters in your first name, what profit did you get for X₁? (value: 20 points)

e. Based on the number of characters in your last name, what profit did you get for X₂? (value: 20 points)

f. What is the sum of your profits for X₁ and X₂? (value: 10 points)

Solution

1)2X1 + 4X2 = 80 --------(1)

3X1 + 1X2 = 60 ----------(2) ...... MULTIPLY EQN (2) BY 4 AND WE GET, 12X1 + 4 X2 = 240-----(3)
substract eqn (3) from (1), we get , -10X1= -160 ............. i.e X1= 16.. putting the value of X1 in eqn (1), we get, X2= 12

2)

2X1 + 4X2 = 400------------(1).....Multiply eqn (1) by 50, we get, 100X1 + 200X2 =20000 -------(3)

100X1 + 50X2 = 8000------(2)......

substract (2) from (3),we get 150X2 = 12000 OR, X2=80 and putting X2=80 in eqn (2). we get X1=40

3)

4X1 + 6X2 = 48------------(1).....

4X1 + 2X2 = 12------------(2).....
substract eqn (2) from (1), we get , X2=9 and putting X2=9 in eqn (2). we get X1= - 1.5

a) 3 rd problem.
B) X1= -1.5
C)X2=9
D) I have 7 character in my 1 st name so profit for X1 = -10.5
E) I have 7 characters in my last name, so profit for X2 = 63
F) sum of profit = 52.5