Question

The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packaging. Each type requires 0.4 hours of assembly time, but the machining operations have different processing times, as shown in the table below (in hours per unit). Each machine is available for 150 hours per month, and the current size of the assembly department provides capacity of 200 hours. Each bookcase produced yields a unit profit contribution as shown below.

Standard Narrow Wide

Trimmer 0.2 0.4 0.6

Shaper 0.6 0.2 0.5

Profit $8 $6 $10

Write a linear optimization model (i.e., identify decision variables, objective function and constraints)

Answer 1

Decision variables

x = standard , y = narrow and z = wide

Objective function

Maximize P = 8 x+ 6 y + 10z

Constraints

0.2x + 0.4y + 0.6 z <= 150

0.6x + 0.2y +0.5 z <= 150

0.4 (x+y+z) <= 200

Formulation and Solution using Excel Solver is following

Formula: E2 =SUMPRODUCT(B2:D2,$B$7:$D$7) copy to E2:E5

Refer sensitivity report, Allowable increase in coefficient of Narrow bookcase is 10 (cell G10). Therefore, new optimal solution have to be determined at a price point of 6+10 = 16

Please rate