A Firm Produces Tires by Utilizing Machine-Hours and Labor-Hours The Firm Can Rent a Machine at a Price $10

question 4

Essay

A firm produces tires by utilizing machine-hours and labor-hours. It has the choice of producing through three separate processes using different combinations of inputs. The optimization can be done by undertaking a process singly or in combination. The combination matrix is provided below:
$\begin{array}{cccc} \text { } & \text { Process \( 1\left(X_{1}\right) \) } & \text {Process \( 2\left(X_{2}\right) \) } & \text { Process \( 3\left(X_{3}\right) \) } & \\ \text { Machine-hours } &1&2&3\\ \text { Labor-hours } &3&2&1\\\end{array}$

The firm can rent a machine at a price $10 and hire a labor at a wage $15. The firm needs to produce a minimum target of 50 tires per day.
(a) Formulate and solve a linear programming problem which will minimize the firm's daily cost (C).
(b) Find out the number of binding constraints in this problem.

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Definitions:

Direct Labor-Hours

The sum of the hours spent by workers directly manufacturing a product.

Variable Overhead

Indirect production costs that fluctuate with the level of output, such as utilities or materials used in the manufacturing process.

Efficiency Variance

A measure used in cost accounting to evaluate the efficiency of resource usage, calculated as the difference between actual usage and the standard or expected usage.

Materials Price Variance

The variance between the standard cost and the actual expense of materials, calculated by multiplying the amount bought.