The monthly output P of a light bulb factory is given by the formula P=400LK, wh

Question

The monthly output P of a light bulb factory is given by the formula P=400LK, where L is the amount invested in labor and K the amount invested in equipment (in thousands of dollars). If the company needs to produce 14,000 units per month, how should the investment by divided among labor and equipment to minimize the cost of production? The cost of production is L + K.

Invested in labor $____?

Invested in equipment $____?

Explanation / Answer

p=14000uts => 14000=400LK => L=35/K minimize cost = L+K or cost = 35/K+K Differentiate cost and equate it to zero on solving we get L=K=sqrt(35) = $5.92(rounded to two decimals)

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