Question

BC Glass Company makes high quality glass products. They make the following two products.
A) Product A: Glass doors with aluminum frames
B) Product B: Glass windows with wooden frames
BC Glass Co. obtains the parts needed for these two products from 3 different manufacturing plants, but in limited quantity.
1) 4 batches of aluminum frames from Plant 1.
2) 12 batches of wooden frames from Plant 2
3) 18 batches of glass frames from Plant 3.
The company uses the parts from the 3 plants to produce their Products A and B. The number of batches of parts needed to make one batch of Products

Answer 1

is this the question, "The number of batches of parts needed to make one batch of Products" ?

Answer 2

BC Glass Company makes high quality glass products. They make the following two products.
A) Product A: Glass doors with aluminum frames
B) Product B: Glass windows with wooden frames
BC Glass Co. obtains the parts needed for these two products from 3 different manufacturing plants, but in limited quantity.
1) 4 batches of aluminum frames from Plant 1.
2) 12 batches of wooden frames from Plant 2
3) 18 batches of glass frames from Plant 3.
The company uses the parts from the 3 plants to produce their Products A and B. The number of batches of parts needed to make one batch of Products A and B are given in the following table.

Products
A
No. of batches of parts needed
Plant 1:(1)
Plant 2:(0)
Plant 3:(3)
Revenue per batch of Product (in thousands): ( $3 thousands)


Product
B
No. of batches of parts needed
Plant 1:(0)
Plant 2:(2)
Plant 3:(2)
Revenue per batch of Product (in thousands):($5 thousand)

Thus, one batch of Product A needs one batch of aluminium frames from Plant 1 and 3 batches of glass frames from Plant 3, while one batch of Product B needs 2 batches of wooden frames from Plant 2 and 2 batches of glass frames from Plant 3. Notice that Products A and B will compete for production of glass frames from Plant 3.
The table also shows the revenue BC Glass Co. obtains for each batch of Product A and B that it makes and sells. Using the limited quantity of parts, BC Glass Co. wants to make and sell a combination of Products A and B to maximize the total revenue.
Question:
(i) Write an optimization problem that will help BC Glass Co. maximize its total revenue. Explain the interpretation of each objective and constraint in the optimization problem.
(ii) If you are the production manager at BC Glass Co., how would you solve the optimization problem? You boss doesn’t know how to solve it, (and we have not learnt this in class), but he has heard about some keywords that may help you solve the problem: linear programming, simplex method, graphical method.
Your task is to search online (e.g. Google) for a method to help you solve the problem, and report your findings to your boss.
• Summarize what you found and evaluate if what you found will be useful for solving the optimization problem from Part (i).
(Tip: You will find some of the keywords more useful than others.)

(iii) (∗) Use what you found to solve the optimization problem in Part (i).