Problem:
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 items 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 (MINUTES)
|
|
Item
|
Profit/Unit
|
Cutting
|
Gluing
|
Finishing
|
|
Chopping board
|
$2k
|
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.
Required:
Question 1) Determine the optimal quantities of the decision variables.
Question 2) Which resources are not completely used by your solution? How much of each resource is unused?
Solve the given numerical problem and illustrate step by step calculation.