A beer manufacturing company has three plants and three warehouses. The bottled beer is made in the plants and sold from the warehouses. The three plants warehouses are in FL, NY and WA. The TX plant the AZ plant can make up to 300 bottles of beers in a month; and the CA plant can make at most 200 bottles of beer in a month. Moreover, the company knows the sales potential of FL warehouse to be 150 bottles per month, NY warehouse to be 350 bottles per month and WA warehouse to be 200 bottles per month. The sales revenues per bottle are: $11, $15 and $13 at FL, NY and WA warehouses, respectively. The cost of shipping from each plant to each warehouse is shown in the following table: are in TX, AZ and CA. The three can make at most 100 bottles of beer in a month;
Cost (S) To Warehouse
From Plant FL NY WA
TX 6 10 9
AZ 8 11 8
CA 9 12 6
Furthermore, the manager of the company has two special requests from the shipping crew:
The total number of bottles that are shipped from TX to FL and WA to be exactly third of the number of bottles that NY received one.
Number of bottles that are shipped from CA to FL must not be lower than any other outgoing shipments from CA.
Number of bottles that are shipped from CA to WA must not be higher than any other outgoing shipments from CA
Lastly, there’s one more set of restrictions that the company must deal with, which is the state regulations on the size of the boxes that can be used in each plant to ship the bottles of beers. Such that, TX plant can only use 5 bottle-boxes (that is, TX can only produce – and ship, bottle amounts that are multiples of 5), AZ plant can only use 6 bottle-boxes and CA plant can only use 4 bottleboxes. Manager of this company aims to maximize profits. Through the parts below, please represent manager’s problem as a linear program.
Could someone who understands this please respond?
(a) List and explain carefully what the decision variables are (in BOXES).
(b) Write out the objective function of the linear program.
(c) Write out the constraints of the linear program.