Question

A wood products firm uses available time at the end of each week to make goods for stock. Currently, two products on the list of times are produced for stock: a chopping board and a knife holder. Both items require three operations: cutting, gluing, and finishing. The manager of the firm has collected the following data on these products:
TIME PER UNIT (MINUTE)
Item profit/unit cutting gluing finishing
Chopping board $2 1.4 5 12
Knife holder $6 0.8 13 3

The manager has also determined that, during each week, 56 minutes are available for cutting, 650 minutes are available for gluing, and 360 minutes are available for finishing.
a. Determine the optimal quantities of the decision variables.
b. Which resources are not completely used by your solution? How much of each resource is unused (c) Set up completed LP model for above problem. (d) Based on your analysis of these quantitative data and your model, what conclusions can you reach and recommend to the manager of this company?

e) If the manager challenges your recommendations, what quantitative evidence would you present to explain and to justify these recommendations?

Answer 1

Answer:

Let board = X1 holder= X2

Max = 2X1+6X2

Subject to: 1.4X1+0.8X2≤56 …………… (1)

5X1+13X2≤ 650 ………………. (2)

12X1+3X2≤ 360 ………………. (3)

a) The solution at point A X1=0 X2=50

Z= 2(0) +6(50) = 300

b) Cutting: 56- 0.8(50) = 15 minutes. (40,0) (0,70) ………… (1)

Gluing: 13X50=650 650-650=0 (130,0) (0,50) …………… (2)

Finishing: 3X50=150 360-150=210 minutes. (30,0) (0,120) ………… (3)

Explanation

See figure in attached file