This question is about the Factory Planning problem that is explained in the

slides of the course. In the general case of this problem, products $=\{1,...,||\}$ must be produced using

processes $=\{1,...,||\}.$ The following parameters and variable are used by an operations research

analyst to formulate the problem:

Parameters:

$$ : The market limit for product $.$

$$ : The per$-$unit profit for selling product $.$

$$ : The total available time for process $($in hour$)$

$$ : The required time of process $$ for one unit of product $($in hour$)$

Variables:

$$ : The number of product $$ produced and sold in the market.

Using this notation, the following model is proposed by the operations research analyst.

$$

$$ in $$

$(1)$

$$

$$ in $$

$<=$ in $(2)$

$0<=<=$ in $(3)$

$$ integer $$ in $(4)$

The data for this problem are given in Factory$\_$Planning.xlsx$.$

Question $1-$Part a$)$ Report the Solution time, the obtained objective value, and the obtained solution.

Question $1-$Part b$)$ The business owner has realized that she has two options;

$1)$ pay $$10,000$ to have $10\%$ more available time for the available time of process $1.$

$2)$ Stick the available times for processes as in the previous part of the question and do not pay

anything.

Which option do you recommend to the business owner?This question is about the Factory Planning problem that is explained in the

slides of the course. In the general case of this problem, products $=\{1,...,||\}$ must be produced using

processes $=\{1,...,||\}.$ The following parameters and variable are used by an operations research

analyst to formulate the problem:

Parameters:

$$ : The market limit for product $.$

$$ : The per$-$unit profit for selling product $.$

$$ : The total available time for process $($in hour$)$

$$ : The required time of process $$ for one unit of product $($in hour$)$

Variables:

$$ : The number of product $$ produced and sold in the market.

Using this notation, the following model is proposed by the operations research analyst.

$$

$$ in $$

$(1)$

$$

$$ in $$

$<=$ in $(2)$

$0<=<=$ in $(3)$

$$ integer $$ in $(4)$

The data for this problem are given in Factory$\_$Planning.xlsx$.$

Question $1-$Part a$)$ Report the Solution time, the obtained objective value, and the obtained solution.

Question $1-$Part b$)$ The business owner has realized that she has two options;

$1)$ pay $$10,000$ to have $10\%$ more available time for the available time of process $1.$

$2)$ Stick the available times for processes as in the previous part of the question and do not pay

anything.

Which option do you recommend to the business owner?