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.)

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Definitions:

Overhead Costs

Expenses related to the operation of a business that are not directly tied to a specific product or service, such as rent, utilities, and administrative expenses.

Activity-Based Costing

A costing method that assigns overhead and indirect costs to specific activities related to the production of goods or services for more accurate cost management.

Activity Rates

The cost driver rates used in activity-based costing to allocate overhead costs to products or services.

Fabricating

The process of creating something by assembling or combining various components, often used in manufacturing and industrial contexts.