Complete the following problems:
1) Review the airline tickets example from pages 1 and 2 of the textbook. Identify two more feasible alternatives. For each feasible alternative you identify, calculate the cost for the alternative and then identify whether these alternatives yield better costs when compared to the three alternatives given in the textbook.
2) Review the maximum area of a rectangle example on page 2 of the textbook. Identify two more feasible solutions and calculate the area for each of these choices of width and height. On page 2, the textbook states "Using differential calculus, the best solution of this model is ". Use calculus to demonstrate how that solution is found. The solution doesn't need to be presented formally but I would like to see all of the steps identified and calculated. Finally, compare the two solutions you found to this optimal solution.
3) Abby, Bridget, Calli, and Debbie are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Abby, being the most athletic, can row across the river in 2 minutes. Bridget, Calli, and Debbie would take 3, 8, and 14 minutes, respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
a. Identify at least two feasible plans for crossing the river (remember, the canoe is the only mode of transportation, and it cannot be shuttled empty).
b. Define the criterion for evaluating the alternatives.
c. What is the smallest time for moving all four people to the other side of the river? In other words, what is the optimal solution?
4) The squares of a board of 10 rows and 10 columns are numbered sequentially 00 through 99 with a hidden monetary reward between $0 and $10 assigned to each square. A game using the board requires the player to choose a square by selecting any two-digit number and then subtracting the sum of its digits from the selected number. If numbers 1-9 are chosen, use a leading zero in the 10's position, i.e 06 for the number 6. The player then receives the reward assigned to the selected square.
a. What monetary values should be assigned to the 100 squares to minimize the player's reward (regardless of how many times the game is repeated)? Be sure to clearly explain how/why you know this (i.e. what calculations did you do to prove this). To make the game interesting, the assignment of $0 to all squares is not an option.
b. Assume you charge $5 to play this game at a fair. Identify a way to assign monetary rewards so that the player feels that the game is fair and continues to play but you (as the one running the game) continue to make money.
5) Describe one example from your personal experience in which you performed an optimization. (Perhaps, in the past, you never realized that you were actually optimizing!) Describe the situation "informally" using the language and new terms introduced in this first chapter and the first commentary. You don't need to provide the solution to this problem. I'm just looking for informal examples in this assignment.
a. Language, such as objective function, constraints, decision variables, maximize, minimize, etc. must be used or points will be deducted.
b. If your homework group has 4 group members, then I would expect to see 4 personal experiences attached to your Lesson 1 Homework submission. These examples must be submitted as part of the Lesson 1 file. If not, credit will not be given.
c. Please write your name at the start of your personal optimization experience (or work it into the first sentence). For example, 'Ryan has used optimization.
Attachment:- Assignment.rar