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Question 423354: your company has a small manufacturing plant that makes three types of bags for selling your cookies: 8 oz, 16 oz, and 32 oz bags. Each bottle requires the service of three departments: filling, labeling, and packaging. The filling, labeling, and packaging departments are allowed to use a total of 380, 330, and 120 person-hours per week, respectively. The time requirements for each bag type and department are specified in the table below. Determine how many of each type of bag your company must produce each week for the plant to operate at full capacity.
---------------------Time (hours)--------------
Department---8 oz Bag----16 oz Bag----32 oz Bag
Filling----------0.6----------1.0------------1.5
Labeling-------0.6----------0.9------------1.2
Packaging----0.2----------0.3------------0.5
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi
8 16 32 Wkly Time
Filling 0.6 1 1.5 380
labeling 0.6 0.9 1.2 330
packaging 0.2 0.3 0.5 120
1.4 2.2 3.2 830
Determine how many of each type of bag your company must produce each week
for the plant to operate at full capacity
Letting x,y,z represent the number of 8,16 and 32oz bags respectively...
Sets Up the Three Equations:
0.6x + y+ 1.5z =380
0.6x + 0.9y + 1.2z =330
0.2x + 0.3y + 0.5z =120
Solving for x, y z...results are: x = 50, y = 200 and z = 100
CHECKING our Answer***
1.4*50 + 2.2*200 + 3.2*100 = 830hrs
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