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Linear programming problem.

I. Choose the best answer for each multiple choice. Please use CAPITAL letters to indicate your answer and write neatly. (20 points)

  1. _ 3. 5. 7. 9. ___
  2. _ 4. 6. 8. 10.___
  3. Which of the following is a valid objective function for a linear programming problem?
    A. Max 5xy
    B. Min 4x + 3y + (2/3)z
    C. Max 5×2 + 6y2
    D. Min (x1 + x2)/x3
  4. Which of the following statements is NOT true?
    A. A feasible solution satisfies all constraints.
    B. An optimal solution satisfies all constraints.
    C. An infeasible solution violates all constraints.
    D. A feasible solution point does not have to lie on the boundary of the feasible region.
  5. Innis Investments manages funds for a number of companies and wealthy clients. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. According to Innis’s risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. Which is the objective function for this problem?
    A. Max 8S + 3M
    B. Max 8S + 3M – 1.2X
    C. Min 8S + 3M
    D. Min 8S + 3M – 1.2X
  6. A solution that satisfies all the constraints of a linear programming problem except the nonnegativity constraints is called
    A. optimal.
    B. feasible.
    C. infeasible.
    D. semi-feasible.
  7. Slack
    A. is the difference between the left and right sides of a constraint.
    B. is the amount by which the left side of a ≤ constraint is smaller than the
    right side.
    C. is the amount by which the left side of a ≥ constraint is larger than the
    right side.
    D. exists for each variable in a linear programming problem.

Sample Solution

Social media has become such an integral part of modern society that the way in which we represent ourselves online has become important above all else. Social media platforms, such as Facebook, Snapchat, Instagram, Tumblr, and Twitter, each present manners for us to represent ourselves and to form a unique identity online. Snapchat, specifically, allows a person to send pictures (snapchats or “snaps) to specific friends for a limited amount of time before they disappear indefinitely or to post a picture for all of their friends to see for a period of 24 hours on their “story”. As Snapchat has grown since its initial release in 2011, they have continued to add on new features, for example, colored lenses allowing a snapchatter to change their pictures to black and white or add a tint. In 2015, Snapchat introduced the “Lens” feature which involves face-altering technology allowing Snapchatters to change how they appear by accentuating certain features or placing computer-generated animal ears, glasses, hearts, etc over their faces. Since the creation of Lenses, many snapchat users have adapted to using these with every single snap that is sent, which is altering how they represent their realities. Before moving further into the analysis and significance of these lenses it is important to look further into the origin. The first lens released was a face altering lens in which the snapchatter was given big eyes, rosey cheeks, and when they opened their mouth, a rainbow would flow out. The introduction of lenses is related to the idea of augmented reality. Augmented reality is when real world objects, in this case the face of the snapchatter, are altered by technology providing a computerized view of the real world. Snapchat bought this face-altering technology from another small company called Looksery and immediately integrated it into their app, and while they are now not the only social media platform to have lenses, theirs are unique in the high definition and ability to truly alter a user’s face.
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