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.

Question

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.

Quizplus · Accepted Answer

The Answer of 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.

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