SOLUTION: How many packs of each hot dogs should be made to maximize profits and what is the profits? all-beef hot dogs - 1 package requires 1 lb of beef regular hot dogs - 1 package req

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Question 110305: How many packs of each hot dogs should be made to maximize profits and what is the profits?
all-beef hot dogs - 1 package requires 1 lb of beef
regular hot dogs - 1 package requires 1/2 lb of beef and 1/2 lb of pork
40 cent profit on each package of all-beef hot dogs
30 cent profit on each package of regular hot dogs
200 lbs of beef and 150 lbs of pork are available

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
x = packages of reg hotdogs produced
y = packages of beef hotdogs produced
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all-beef hot dogs - 1 package requires 1 lb of beef
regular hot dogs - 1 package requires 1/2 lb of beef and 1/2 lb of pork
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200 lbs of beef and 150 lbs of pork are available
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y%5Bmax%5D = 200 lbs / 1 lb
y%5Bmax%5D+=+200
x%5Bmax%5D = 150 lbs / .5 lbs
x%5Bmax%5D+=+300 This is because once you run out of pork, the leftover
beef does you no good
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x+=+0
y%5Bmax%5D+=+200 This is the most y can be
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x+=+50
y%5Bmax%5D+=+175 this is 200 - 25
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x+=+100
y%5Bmax%5D+=+150 this is 200 - 50
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x+=+150
y%5Bmax%5D+=+125 this is 200 - 75
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x+=+200
y%5Bmax%5D+=+100 this is 200 - 100
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x+=+250
y%5Bmax%5D+=+75 this is 200 - 125
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x+=+300
y%5Bmax%5D+=+50 this is 200 - 150
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Now list the profit in each case
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.3%2A0+%2B+.4%2A200+=+80
.3%2A50+%2B+.4%2A175+=+85
.3%2A100+%2B+.4%2A150+=+90
.3%2A150+%2B+.4%2A125+=+95
.3%2A200+%2B+.4%2A100+=+100
.3%2A250+%2B+.4%2A75+=+105
.3%2A300+%2B+.4%2A50+=+110
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It looks like 300 packages of regular and 50 packages of beef
hotdogs will maximize profit at $110
To verify, I'll look at profits with a change of 2 packages for x
.3%2A298+%2B+.4%2A51+=+109.8
So it looks like $110 is the maxprofit