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Math Help - Can any1 help me with this example...?

  1. #1
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    Can any1 help me with this example...?

    I ould really do with some help on this example i got in a revision booklet i have. Any input is great...thankyou.

    product 1 needs 0.3 of A
    0.1 of B

    product 2 needs 0.2 of A
    0.1 of B
    0.1 of C

    At most there is 1400 units of A, 500 units of B, and 400 units of C
    Profit = 0.90 on each product 1 and 1.00 on each product 2.
    If product 1 = X and product 2 = Y,

    1)Show that they can make an profit(p) of at least P = 0.9X + Y
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  2. #2
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    Hello, Bobby!

    Product 1 needs: 0.3 of A and 0.1 of B

    Product 2 needs: 0.2 of A, 0.1 of B, and 0.1 of C

    At most there is 1400 units of A, 500 units of B, and 400 units of C.

    Profit = 0.90 on each Product 1 and 1.00 on each Product 2.

    Let x = number of Product 1, y = number of Product 2.

    1) Show that they can make an profit (P) of at least: . P \:= \:0.9x + y . ?
    I don't understand the question . . .
    . . I'll give the standard Linear Programming solution.


    Organize the given information . . .

    \begin{array}{cccccccc}<br />
& | & A & | &  B & | & C & | \\ \hline<br />
\text{Product 1 }(x) & | & 0.3x &|& 0.1x &| &  & | \\<br />
\text{Product 2 }(y)  & | & 0.2y &|& 0.1y &|& 0.1y & | \\ \hline<br />
\text{Available} & | & 1400 & | & 500 & | & 400 & | \end{array}

    We have these inequalities: . \begin{array}{cccc}0.3x + 0.2y & \leq & 1400 & [1]\\ 0.1x + 0.1y & \leq & 500 & [2]\\ 0.1y & \leq & 400 & [3]\end{array} . . . . also: . x \geq 0,\;y \geq 0

    Graph the region indicated by these inequalities.
    Determine the vertices of the resulting polygon.

    Test the vertices in the profit function
    . . to see which gives us maximum profit.

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  3. #3
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    Joined
    Nov 2007
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    Cheers for the reply....sorry if i dodn't explain it properly, the whole question is as follows....

    A breakfast cereal manufacturer makes two different types of cereal, Golden Oldies and Crunchy Bites. Each box of Golden Oldies requires 0.3kg of wheat and 0.1kg of vitamin-enriched syrup, and each box of Crunchy Bites requires 0.2kg of wheat, 0.1kg of sugar and 0.1kg of vitamin-enriched syrup. Suppliers can deliver at most 1400kg of wheat, at most 400kg of sugar and at least 500kg of the vitamin-enriched syrup per week. The profit is 0.90 on each box of Golden Oldies and 1.00 on each box of Crunchy Bites.
    Let X and Y denote the number of boxes of Golden Oldies and Crunchy Bites the manufacturer can produce per week.
    (a) Show that the manufacturer can make a weekly profit of 0.9X + Y
    (b) Write down all the constraints for the problem.
    (c) Solve the linear programming problem graphically to find the number of boxes of each type of cereal that maximise the profit. On your graph indicate clearly the feasible region, the optimal point, an arbitrary isoprofit line, and the isoprofit line corresponding to optimal profit.
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