helpMANAGEMENT SCIENCE $1$

PROJECT $($B$)$

PROBLEM

The Flair Furniture Company produces inexpensive tables and chairs. The

production process for each is similar in that both require a certain number of

labor hours in the carpentry department and a certain number of labor hours

in the painting department. Each table takes $3$ hours of carpentry work and $2$

hours of painting work. Each chair requires $4$ hours in carpentry and $1$ hour in

painting. During the current month, $2400$ hours of carpentry time and $1000$

hours of painting time are available. The marketing department wants Flair to

make no more than $450$ new chairs this month. However, because the existing

inventory of tables is low, the marketing department wants Flair to make at

least $100$ tables this month. Each table sold results in a profit contribution of

$$7,$ and each chair sold yields a profit contribution of $$5.$

Determine the decision variables.

Determine the constraints.

Formulate a linear programming model.

Define:

a$)$ Optimum solution

b$)$ Optimum value

c$)$ Slack variable

d$)$ Range of Optimality

e$)$ Range of Feasibility

f$)$ Shadow Price

g$)$ Binding Constraints

h$)$ Non$-$binding constraints

i$)$ Feasible Region

Transform the linear programming model in $(3)$ to standard form.

Using graphical method analyse the phrases defined in $(4)$

Using QM software find the phrases defined in $(4)$

In graphical method analysis, when it comes to simultaneous changes for

coefficients of objective function:

a$)$ Give one example where the optimal solution is applicable

b$)$ Give one example where the optimal solution is not applicable

In graphical method analysis, when it comes to simultaneous changes for

RHS of constraints:

a$)$ Give one example where the shadow price is applicable

b$)$ Give one example where the shadow price is not applicable

Interpret all your finding correspond to the problem given.