Homework SoursePart 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)
| 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
My name is ,say, John Players
Problem 2:
2X1 + 4X2 = 400 …(1)
100X1 + 50X2 = 8000 ….(2)
Let us multiply both the sides of the 1st equation by 50. Then we get 100X1 + 200X2 = 20000…(3)
Now, on subtracting the 3rd equation from the 2nd equation, we get, - 150X2 = -12000 so that X2 = 80.
On substituting X2 = 80 in the 1st equation, we get, 2X1 + 4 * 80 = 400 or, 2X1 = 400 - 320 = 80 so that X1 = 80/2 = 40. The solution is X1 = 40and X2 = 80.
Step 2: My first is 4 characters long and my last name is 7 characters long. So, the profit for X1 and the profit for X2 would be as under:
Profit for X1 = 4 *40 = $ 160
Profit for X2 = 7*80 = $ 560
Step 3:
a. Problem 2
b. X1 = 40,
c. X2 = 80
d. Profit for X1 = $ 160
e. Profit for X2 = $ 560
f. Sum of the profits for X1 and X2 = $ 160 + $ 560 = $ 720
