$\lambda$ -Ranger Construction Is Preparing to Repair Potholes, Under Contract to to the Local

question 41

Essay

$\lambda$
-Ranger Construction is preparing to repair potholes, under contract to the local county road repair agency. Based on past experience, Ranger has found that output can be described by: Q = K^.5L^.5, where Q = pot holes filled, K = units of capital, and L = units of labor. Ranger can hire labor at $12 per hour, and the cost of capital is $8 per unit. Capacity limitations require that Ranger accepts no more than $96,000 worth of filling this season. What is the optimal mix of inputs for Ranger? How many potholes should Ranger agree to fill? Use the method of Lagrange multipliers to find the solution.

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Definitions:

Stem-And-Leaf

A graphical representation that organizes data points by splitting each value into a "stem" (the leading digit or digits) and a "leaf" (the final digit).

Skewed

A description of a distribution that is not symmetrical, with a longer tail on one side of the peak than on the other, often indicating the presence of outliers.

Profits

The financial benefit that is realized when the amount of revenue gained from a business activity exceeds the expenses, costs, and taxes involved in sustaining that activity.

Outliers

Data points that significantly deviate from the rest within a random population sample, appearing at an unusually large distance from other values.