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A company manufactures x units of one item and y units of another. The total cost in dollars, C, of producing these two items is approximated by the function

A) If the production quota for the total number of items (both types combined) is 182, find the minimum production cost.
I solved this one and I got 32541 and that is the right answer.
B)Estimate the additional production cost or savings if the production quota is raised to 183 or lowered to 181.
I am stuck on this problem. I am getting 350.04 savings and 351.96 production cost.

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  1. C=7x^2+xy+1y^2+600
    x+y=182 or y=182-x
    C=7x^2+x(182-x)-(182-x)^2 + 600
    dC/dx=14x +182-x -x -2(182-x)(-1)=0

    solve for x to get I hope 32541 is the answer.

    Then you know dC/dx so dC/dx for x=32541 is figure that from dC/dx at x=32541
    so if you lower x by one, C=32541-dC/dx
    and if you increase by one, C=32541+dC/dx

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  2. caleclat

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