Question 110305
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[max]}}} = 200 lbs / 1 lb
{{{y[max] = 200}}}
{{{x[max]}}} = 150 lbs / .5 lbs
{{{x[max] = 300}}} This is because once you run out of pork, the leftover
beef does you no good
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{{{x = 0}}}
{{{y[max] = 200}}} This is the most y can be
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{{{x = 50}}}
{{{y[max] = 175}}} this is 200 - 25
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{{{x = 100}}}
{{{y[max] = 150}}} this is 200 - 50
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{{{x = 150}}}
{{{y[max] = 125}}} this is 200 - 75
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{{{x = 200}}}
{{{y[max] = 100}}} this is 200 - 100
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{{{x = 250}}}
{{{y[max] = 75}}} this is 200 - 125
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{{{x = 300}}} 
{{{y[max] = 50}}} this is 200 - 150
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Now list the profit in each case
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{{{.3*0 + .4*200 = 80}}}
{{{.3*50 + .4*175 = 85}}}
{{{.3*100 + .4*150 = 90}}}
{{{.3*150 + .4*125 = 95}}}
{{{.3*200 + .4*100 = 100}}}
{{{.3*250 + .4*75 = 105}}}
{{{.3*300 + .4*50 = 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*298 + .4*51 = 109.8}}} 
So it looks like $110 is the maxprofit