Phil Bert's Nuthouse is preparing a new product, a blend of mixed nuts. The product must be at most 50 percent peanuts, must have more almonds than cashews, and must be at least 10 percent pecans. The blend will be sold in one-pound bags
Phil's goal is to mix the nuts in such a manner that all conditions are satisfied and the cost per bag is minimized. Peanuts cost $1 per pound. Cashews cost $3 per pound. Almonds cost $5 per pound and pecans cost $6 per pound. Formulate this problem as a linear program.
Call the variables PN, AL, CA, and PC
Minimize cost = $1PN + $3CA + $5AL + $6PC
subject to
PN + CA + AL + PC = 1 (so that the bag weighs one pound)
PN ? .5 (the one-pound bag must have no more than 50% peanuts)
-CA + AL ? 0 (more almonds than cashews)
PC ? .1 (at least 10% of the one-pound bag must be pecans)
PN, CA, AL, PC ? 0 (non-negativity)
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