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Math Help - Linear Programming-Check

  1. #1
    Junior Member
    Joined
    Oct 2007
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    44

    Exclamation Linear Programming-Check

    I went back and change my answers can I found out I had some of them wrong, can you please check them.

    A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and an ounce of potatoes for $0.02. The dietician is bound by the following constraints.
    ∙ Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates.
    ∙ Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates.
    ∙ The minimum daily requirements for the patients under the dietitian's care are 45 grams of protein and 58 grams of carbohydrates.
    Let x = the number of ounces of chicken and y= the number of ounces of potatoes purchased per patient. Write a system of inequalities that describes these constraints.

    I got:

    13x+5y > than or equal 45
    24x+35 > than or equal to 58

    Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 5 hours to make a hat and 3 hours to make an afghan, and she has no more than 41 hours available. She has material for no more than 11 items, and she wants to make at least two afghans. Let x = the number of hats she makes and y = the number of afghans she makes. Write a system of inequalities that describes these constraints.

    I got:

    5x+3y< then or equal to 41
    x+y< than or equal to 11
    y > than or equal to 2

    An office manager is buying used filing cabinets. Small file cabinets cost $5 each and large file cabinets cost $8 each, and the manager cannot spend more than $72 on file cabinets. A small cabinet takes up 7 square feet of floor space and a large cabinet takes up 10 square feet, and the office has no more than 96 square feet of floor space available for file cabinets. The manager must buy at least 7 file cabinets in order to get free delivery. Let x = the number of small file cabinets bought and y = the number of large file cabinets bought. Write a system of inequalities that describes these constraints.

    I got:

    5x+8y< then or equal to 72
    7x+10y < than or equal to 96
    x+y > than or equal 7

    but I think its this one, but this one doesnt make sense.

    5x+8y< then or equal to 72
    10x+7y < than or equal to 96
    x > than or equal to 7


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  2. #2
    Super Member

    Joined
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    Lexington, MA (USA)
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    Hello, soly_sol!

    1) Chicken/potatoes

    I got: . \begin{array}{ccc}13x+5y & \geq & 45\\<br />
24x+35 & \geq & 58\end{array}
    2) Hats/afghans

    I got: . \begin{array}{ccc}5x+3y & \leq & 41 \\<br />
x+y & \leq & 11 \\<br />
y & \geq & 2\end{array}
    Small/large cabinets

    I got: . \begin{array}{ccc}<br />
5x+8y & \leq & 72 \\<br />
7x+10y & \leq & 96 \\<br />
x+y & \geq & 7\end{array}

    All correct!

    Nice work!


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