# A candy company has 120 kg of chocolate-covered nuts and 90 kg of chocolate-covered raisins to be sold as two different mixes. One mix will contain half nuts and half raisins and will sell for \$7 per kg. The other mix will contain 3/4 nuts and 1/4 raisins and will sell for \$9.50 per kg.   How many kilograms of each mix should the company prepare for the maximum revenue? Find the maximum revenue. Let x represent the number of kilograms of the 1/2:1/2 mix, and y the number of kilograms of the 3/4:1/4 mix. (Here the ratio is nuts to raisins.)

The amount of profit can be represented by P=7x+9.5y.

There are some constraints -- namely the amount of raw materials available. The constraints can be represented by a system of inequalities:

`x>=0,y>=0` are the natural constraints.

`1/2 x+3/4y<=120` represents the amount of nuts available. Each kg of mix x uses 1/2 kg of nuts, while each kg mix y uses 3/4 kg.

`1/2x+1/4y<=90` represents the amount of raisins available.

Graphing the system of inequalities yields a feasible region (in this case a bounded polygon) where every point in the region satisfies all of the inequalities. By the corner point principle, there is a maximum and a minimum for the objective function (the profit function in this case) and they occur at the...

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