Find the maximum production level p = 100x^{0.34}y^{0.66} if the total cost of labor (at $72 per unit) and capital (at $40 per u

Question

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Find the maximum production level p = 100x^{0.34}y^{0.66} if the total cost of labor (at $72 per unit) and capital (at $40 per u

nit) is limited to $270,000, where x is the number of units of labor and y is the number of units of capital. Round your answer to the nearest integer.

Mathematics

1 answer:

Anton [14] · Answer 1 · 2022-07-21T10:07:12+03:00

Maximum production p=552728

Step-by-step explanation:

The equation for maximum production is : $p=100x^{0.34} y^{0.66}$

The number of units of labor is x @$72

The number of units of capital is y @$40

The total cost of labor and capital is limited to $270,000, this can be written as;

72x+40y ≤ $270,000

Graphing the inequality to find values of x and y ,from the graph;

x=3750 units

y=6750 units

Applying the expression for maximum production

$p=100*x^{0.34}* y^{0.66} \\\\p=100*3750^{0.34} *6750^{0.66} \\\\p=552727.56\\\\p=552728$

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Inequalities graphs :brainly.com/question/11386040

Keywords: maximum, production,cost, labor,limited to,capital ,unit

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