How do I write this out?

Question

An office supply manufacturer makes two kinds of paper clips, standard and extra large. To make 1000 Standard paper clips requires 1/4 hour on a cutting machine and 1/2 hour on a machine that shapes the clips. One thousand extra large paper clips require 1/3 hour on each machine. The manager of paper clip production has 4 hours per day available on the cutting machine and 6 hours per day on the shaping machine. How many of each clip can he make?

Answer 1

First, to answer an objection posted by one of the other responders: in general, when a problem fails to state an absolute goal, one may make one or more appropriate assumptions to make a clear goal, though said assumptions should be as few and as simple as possible. I would make the assumption here that the goal is to use all the machine time available, unless it turns out more clips can be made with machine time remaining.

But, regardless, the way to set up the problem is:

for the cutting machine:

the number of batches of Standard clips times ¼ hour plus the number of batches of extra large clips times 1/3 hour equals 4 hours: (call the batches of Standard clips "x" and the batches of extra large clips "y")

1/4*x + 1/3*y = 4

and, for the shaper:

the number of batches of Standard clips times ½ hour plus the number of batches of extra large clips times 1/3 hour equals 6 hours: (call the batches of Standard clips "x" and the batches of extra large clips "y")

1/2*x + 1/3*y = 6

and then solve for x and y.

(x = 8, y = 6: so 8,000 Standard clips and 6,000 extra large clips.)

Answer 2

Extra Large Paper Clips

Answer 3

HE can manufacture 6 large batches (1000ea. ) and 8 small batches (1000ea.). Total is 14,000 clips. That equals 4 hours cutting and 6 hours bending.

Answer 4

There doesn't seem to be any kind of tradeoff involved, such as limits on what can be sold, so he can make a boatload of one kind (whatever the arithmetic turns out to be, but that's simple arithmetic) and zero of the other.

Answer 5

dude, my brain just exploded reading all that