Food-Processing-Plant-Design-layout

Food Processing Plant Design & layout
P ≤ 25,000 T ≤ 20,000
Next, we note that the capacity of our departments is also limited. Suppose both vegetables
are packed in the same type of can, and the can department has a capacity of 30,000 cans
per week. This puts another restriction on our production program.
P + T ≤ 30,000
The preparation department, which operates 40 hours per week, requires 0.001 hours to
process enough peas to fill a can and 0.002 hours to process a can of tomatoes. We then
have a processing department restriction that says
0.001 P + 0.002 T ≤ 40
or
P + 2T ≤ 40,000
The packing department has a capacity of 50,000 cans of either type for the week, giving
P + T ≤ 50,000
One might go on adding restrictions and conditions to make the problem more and more
realistic, but at this point the decision about a production program is sufficiently
complicated to suggest the difficulties that might be encountered.
The problem is still simple enough so that its solution may be graphically illustrated. Any
decision as to a production program can be represented by a point on Figure 6, that is, a
particular pair of values for P and T. By plotting the inequalities which express the
restriction we can see exactly how our choice is limited. Because of the limited production
by farmers our choice of P must lie on or below the horizontal line P = 25,000. Similarly, our
choice of T must lie to the left of a vertical line T = 20,000. The other two restrictions are
similarly plotted, with the result that our decision is limited in fact to P and T combinations
lying in or on the edge of the shaded area in Fig 11.7.
Fig 11.7 Possible production programmes and restrictions
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