Question

A computer company sells 3 types of disks for their line of computer. They are of different qualities and are packaged with different types of accessories. They are sold in lots of 100. Each lot has to be manufactured, checked for errors, and ultimately packaged, each of these taking different amounts of time depending on which type of disk we are considering. The relevant information for each lot of 100 is given in the following table: Each day the company Time (in hours) Disk Type Manufacturing Checking Packaging Profit 2 0 0.1 .2 0.2 $10 $15 $25 12 has available 120 manufacturing hours (12 workers do the manufacturing and each works 10 hours per day), 30 checking hours, and 20 packaging hours. How many lots of each should be made to maximize the profits, assuming that there must be at least 10 lots of the first disk type made, and assuming that the number of lots of type 2 disks be at least twice as many as the number of lots of type 3 disks. (Assume that all lots made can be sold.)

Answer 1

Answer : The combination with the given assumption and to maximise profit is as under

Time in hours					Maximum Profit
Disk type	manufacturing	checking	packing	Profit
1	36	12	1.2	$ 10	120
2	30	10	1	$ 15	75
3	30	7.5	0.5	$ 25	62.5
Utilized	96	29.5	2.7		257.5
Available	130	30	20

Workings

1- We have to do at least 10 lots of Disk Type 1 . Here , we have taken 12 lots of Disk Type 1

2- We have to take twice the lots of Disk 3 for Disk 2. here , we have taken 2.5 lots for Disk Type 3 and 5 lots of Disk typ3 2.

3 - Though it has consumed 96 hrs of Manufacturing , 29.5 hours of Checking and 2.7 hours of Packing

4 - Since we have to follow the assumption of Twice the Lots of Disk Type 3 has to be made for Disk 2 , we can't utilize 34 hrs of Manufacturing , while consumed almost 29.5 hrs out of 30 hrs of Packing and only 2.7 hrs out of 20 hours of Checking.

5 - We know that until a Disk is not only manufactured but duly packed and checked , it cannot be sold. Hence, any other combination of manufacturing given the constraints of 130 hours for Manufacturing , 30 hours for Checking  and 20 hours for packing  is  not feasible.

6 - We assume that idle hours of Packing , cannot be utilized for Checking and vice versa.

Hence, with certain assumptions, we conclude that we can maximize our revenue upto $ 257.5 with the given constraints / assumptions.