a trail mix company has 200 lb of peanuts and 160 lb of raisins. a batch oh house mix takes 20 lb of peanuts and 10 lb of raisins. a batch of fancy mix takes 10 lb of peanuts and 20 lb of raisins. profit from a batch of house mix is $50 and from a batch of fancy mix is $60. how much of each type should be made to maximize profits? what is the maximum profit?
lbspeanuts=20h+10f lbsraisins=10h+20f h=batches of house, f=batches of fancy so we have the inequalities 20h+10f <=200 10h+20f<=160 the profit (p): p=50h+60f so we graph the two inequalities, and find where the profit is maximized.
so how much of each type should be made to maximize the profits? and what is the max profit?
Look at the boundary, and specifically the endpoints in this case, and I think the maximum is where the boundary lines intersect at h=8, f=4 which gives a profit of: 50*8+60*4=400+240=$640
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