Notes: This is an individual closed book/note exam. YOU ARE NOT ALLOWED TO GIVE

Question

Notes: This is an individual closed book/note exam. YOU ARE NOT ALLOWED TO GIVE HELP TO OR RECEIVE HELP FROM OTHER STUDENTS YOU MUST SUBMIT YOUR RESPONSE IN BLACKBOARD Flair Furniture produces two products: tables and chairs. The information for the production of each of these products is given in the following table. There is a total of 2,400 carpentry hours and 1,000 painting hours. What combination of tables and chairs maximizes total profit? Carpentry Painting Product Min Max Profit ($) (hrs) (hrs) Table 100 Chair 4 450 5 a) Formulate the problem as a linear programming model IN A WORD FILE. b) Solve the LP using Excel AND GENERATE THE ANSWER REPORT Hint I: Objective function max TT+5C Hint 2: There are a total of four constraints (excluding non-negativity constraints). Example of a constraint: carpentry hours 3T + 4C

Explanation / Answer

Let no of tables be T and chair be C

Objective function

Max: 7T+5C

Constraints

3T+ 4C 2400

2T+C 1000

C 450

T 100

Both C and T greater than 0

Solution :

Objective Cell (Max) Cell Name Original Value Final Value $E$4 Profit Sum total 0 4040 Variable Cells Cell Name Original Value Final Value Integer $C$3 Required Tables 0 320 Contin $D$3 Required Chairs 0 360 Contin Constraints Cell Name Cell Value Formula Status Slack $E$5 Carpentry hrs Sum total 2400 $E$5<=2400 Binding 0 $E$6 painting Sum total 1000 $E$6<=1000 Binding 0 $C$3 Required Tables 320 $C$3>=0 Not Binding 220 $C$3 Required Tables 320 $C$3>=100 Not Binding 220 $D$3 Required Chairs 360 $D$3<=450 Not Binding 90 $D$3 Required Chairs 360 $D$3>=0 Not Binding 360

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