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

Question

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

radar · Answer

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

anonymous · Answer

were suppose to use Lagrange multiplier and probably Kuhn tucker conditions but thank you

radar · Answer

O.K.  I gotta run, eye exam!  Good luck.