Part of understanding linear programming is knowing how to do the algebra to ide

Question

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 I-P, do problem #2.

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

2X1 + 4X2 = 400

100X1 + 50X2 = 8000

(My first name has 5 letters and my name has 4 letters.)

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)

Explanation / Answer

a) My last name is Lakshmi which ends up with 'I' . So, i solved Problem 2.

b) Byconsidering the equations,

2X1 + 4X2 = 400 ------> (1)

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

multiply equation (1) with 25 and equation (2) with 2

So, we get 25 * (2X1 + 4X2 = 400 ) which gives 50X1 + 100X2 = 10000 -----> (3)

2 * (100X1 + 50X2 = 8000) which gives 200X1 + 100X2 = 16000 --------> (4)

By subtracting equation (3) from the Equation (4) we get

200X1 + 100X2 = 16000  

50X1 + 100X2 = 10000

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150X1= 6000 which implies X1 = 6000 / 150 = 40

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Therefore, X1 = 40

c) By substituting the value of X1 in equation (1) we will get

2* 40 + 4X2 = 400

80 + 4X2 = 400

4X2 = 400-80

4X2= 320

X2 = 320/4 = 80

Therefore value of X2 = 80

d) My First name is Niharika. So, the number of characters = 8

So, profit for X1 = 40 * 8 = $320

e) My Last name is Lakshmi . So, the number of characters = 7

So, profit for X2 = 80 * 7 = $560

f) The sum of profits for X1 & X2 is $320 + $560 = $880

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