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**Someone** on
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-your school club decides to hold a fundraiser by selling trail mix, and you are in chrage of making the mix. You plan to offer two mixes, Country Blend and Premium Mix, each sold in one pound bags. Each pound of Country Blend consists of 1/2 pound of toasted oats, 1/4 pound of peanuts, and 1/4 pound of raisins. Each pound of Premium Mix consists of 1/4 pound of toasted oats, 1/4 pound of peanuts, and 1/2 pound of raisins. You have available to use at most 40 pounds of oats, 22 pounds of peanuts, and 35 pounds of raisins.

1. Model the situation above by letting X represent the # of pounds of Country Blend and Y represent the # of pounds of Premium Mix. Your algebraic model should be a system of five inequalities.

2. Graph it.

3. You sell the trail mix for $5 per pound for Country Blend and $7 per pound for Premium Mix. How many bags of each type of mix should you make it order to maximize your income? (The maximum income must occur at one of the vertices of the graph.)

4. Using the answer from #3, what will be your club's income if all the bags of mix are sold?