Consider the Objective Function $Y=A \times L^{\alpha} \times K^{\beta}$

question 23

Essay

Consider the objective function,
$Y=A \times L^{\alpha} \times K^{\beta}$
where,
Y = total output
A= total-factor productivity
L = labor input
K= capital input
α = capital input share of contribution for L
β = capital input share of contribution for K
a. Assume α = 0.33, β = 0.67, A = 10 and each unit of labor costs $45 and each unit of capital costs $55. With $50,000 available in the budget, develop an optimization model to determine the number of units of capital and labor required in order to maximize output.
b. Find the optimal solution to the model you formulated in part a. Round all your answers to two decimal places. (Hint: When using Excel Solver, use the Multistart option with bounds 0 ≤ L ≤ 700 and 0 ≤ K ≤ 1000.)

Analyze process stability and capability using statistical tools.

Identify the need for process adjustments based on statistical analyses.

Understand acceptance sampling and its application in quality control.

Calculate and analyze the Average Outgoing Quality (AOQ) in acceptance sampling.

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Definitions:

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