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

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.