Question

The company wants to increase the available products from 2 types of glasses to 3 types. A production line already produces 2 different types of glasses: 6oz juice glasses and 10oz cocktail glasses and 8oz champagne glass. Adding a new type is possible but you as a manager should check that it will be cost effective. The production line can produce 100 cases of 6oz glasses in 6 hours and 100 cases of 10oz glasses in 5 hours. The production time for the new type, a champagne glass, is 8 hours per 100 cases. A manager needs to optimize the production while she prefers to operate the line on a schedule of 60 hours per week. The product is stored in factory’s storage room with the capacity of 15000 cubic feet. A case of 6oz glasses requires 10 cubic feet and a case of 10oz glasses requires 20 cubic feet. A case of the 8oz champagne glass requires 10 cuft. A retail customer will buy 6oz glasses for $5.00 per case but can accept only 800 cases per week and 10oz glasses for $4.50 per case, and 8oz glasses for $6.00 per case and there is no limit on the size of the order for these two types.

1.(10 points) Find how how many cases of each type of glass should be produced each week in order to maximize the profit ? Note: In the report display the optimal solution and the objective function value clearly in a form of a table. 2. (3 points) Is including a new type of glass (the champagne glass) economically attractive ? 3. (5 points) Determine shadow prices summarize them in a table and associate correct units with them. 4. (2 points) If you divert resources to produce extra one hundred cases of 8oz champagne glasses how much would the profit change ? (this quantity is called reduced cost).

Answer 1

Option 1 :-

100% production of 10 Oz juice glasses

Highest production possible with these glasses is 750 classes as producing 750 classes would consume all 15,000 cubic feet space using 37.5 as for production and letting know for the space for any extra production.

Revenue earned = 750*4.5=$3375

Option 2 :-

Producing 100% production of of 8 Oz champagne glasses

Producing 100% champagne glasses would consume 56 hours to produce 750 units of champagne glasses, however it will consume all 60 hours that are been provided for the total production and the only revenue generated would be 6*750 = 4500$

Option 3 :-

Thus the most optimal option is to produce 6 Oz juice glasses at hundred percent production level because even after reducing 100% capacity of 6 Oz juice glasses there be much space left as well as time left to produce other glasses

Maximum production capacity - 800 glasses

Time = 48 hours .

Remaining time = 60-48=12 hours

Space utilised = 10*800=8000 cubic feet

Remaining space = 15000-8000=7000 cubic feet .

Revenue earned = 5*800=$4000

The following schedule shows that what are the various production possibilities left that can be divided between 8 Oz champagne glasses and 10 Oz juice glasses

Combination	8 oz glasses	10 oz glasses	Total revenue earned
A	0	240	240*4.5=$1080
B	100	80	600+360=960
C	120	75	540+450=930
D	150	0	150*6=$900

Now the most profitable option for the firm is to produce 800 glasses of 6 Oz juice and with the remaining time left it should produce 240 glasses of 10 Oz juice amounting to a total revenue of dollar 5080.

However as 8 Oz champagne glasses are being included in the the production assembly therefore the extra value on using the left 12 hours after the production of 6 Oz classes is combination be that is Dollar 960 .

The revenue on bhaiya not including the champagne glasses is Dollar 5080 while the revenue on after including the champagne glasses in the production assembly is Dollar 4960 result into a loss of profit of dollar 120.

Therefore the production of 8 Oz champagne glasses and its inclusion in the production assembly line is not an economically viable option for the company .