constrained optimization involving multivariate functions A furniture company makes personal computer stands. For a certain model, the total cost (measured in thousands of dollars) when q hundred stands are produced is given by C(q) = 2q3 - 9q2 + 12q + 20 The company is currently capable of manufacturing between 75 and 600 (inclusive) per week. Determine the number of stands that must be produced so as to minimise total cost

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constrained optimization involving multivariate functions A furniture company makes personal computer stands. For a certain model, the total cost (measured in thousands of dollars) when q hundred stands are produced is given by C(q) = 2q3 - 9q2 + 12q + 20 The company is currently capable of manufacturing between 75 and 600 (inclusive) per week. Determine the number of stands that must be produced so as to minimise total cost

Mathematics
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dC/dq=6q^2-18q+12 set 6q^2-18q+12+0 divide thru by 6 q^2-3q+2=0 solve by factoring (q-2)(q-1)=0 solve for q q=2 q=1 test each solution for minimum 2q-3=0 taking derivative of the derivative 2(2) -3 = 1 is positive, so is a minimum answer is 200 units
were suppose to use Lagrange multiplier and probably Kuhn tucker conditions but thank you
O.K. I gotta run, eye exam! Good luck.

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