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A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of​ protein, 3 units of​ carbohydrates, and 2 units of​ fat, and will contain 30 calories. Each ounce of nuts will supply 2 units of​ protein, 2 units of carbohydrates​, and 4 units of​ fat, and will contain 40 calories. Every package must provide at least 4 units of​ protein, at least 10 units of​ carbohydrates, and no more than 18 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of​ calories?

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  1. you want to minimize c=30f+40n subject to
    0f+2n >= 4
    3d+2n >= 10
    2f+4n <= 18
    plot the lines and evaluate c at the vertices.

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