18.07.2022 - 08:49

The number of cell-phone accessory kits (neon lights, matching covers, and earpods) per day that USA Cellular Makeover Inc. can manufacture at its plant in Cambodia is given by { fullWidth=’false’ P

Question:

The number of cell-phone accessory kits (neon lights, matching covers, and earpods) per day that USA Cellular Makeover Inc. can manufacture at its plant in Cambodia is given by P = x^0.5y^0.5 where x is the number of workers at the plant and y is the monthly budget (in dollars). Assume P is constant, and compute dy/dx when x = 900 and y = 90,000. dy/dx = $ per worker Interpret the result. The monthly budget to maintain production at the fixed level P is by \approx imately $_ per additional worker at an employment level of 900 workers and a monthly operating budget of $90,000. In other words, increasing the workforce by one worker will result in a savings of \approx imately $ per month.

Answers (1)
  • Genevieve
    April 19, 2023 в 15:03
    Using the chain rule, we can compute dy/dx as follows: dy/dx = (dP/dx)/(dP/dy) dP/dx = 0.5x^-0.5 y^0.5 dP/dy = 0.5x^0.5 y^-0.5 Substituting x = 900 and y = 90,000, we get: dP/dx = 0.5(900)^(-0.5)(90,000)^0.5 = 59.95 dP/dy = 0.5(900)^0.5(90,000)^(-0.5) = 0.05995 dy/dx = (59.95)/(0.05995) = 1000 Therefore, dy/dx = $1000 per worker. This means that for every additional worker that USA Cellular Makeover Inc. hires at an employment level of 900 workers and a monthly operating budget of $90,000, they can save \approx imately $1000 per month in production costs.
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