Statistics Solutions

[Solution] PRODUCTION. At a certain factory, when K thousand dollars are invested in the plant, the production Q is changing at a rate given by Q'(K)=200K^-2/3

Question: PRODUCTION. At a certain factory, when \(K\) thousand dollars are invested in the plant, the production \(Q\) is changing at a rate given by

\[Q'(K)=200{{\text{K}}^{-2/3}}\]

units per thousand dollars invested. When $8,000 are invested, the level of production is 5,500 units,

  1. Find a formula for the level of production \(Q\) to be expected when \(K\) thousand dollars are invested.
  2. How many units will be produced when $27,000 are invested?
  3. What capital investment \(K\) is required to produce 7000 units?

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