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Calculus

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
C=7x^2+xy+1y^2+600.

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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    bobpursley
  2. caleclat

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