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Planters Nut Company

Planters Nut Company is planning to launch a new $32-$ounce can of mixed nuts. The product will be a mix of Cashews, Almonds, Walnuts, Pecans, Brazil Nuts, Macadamia Nuts, Peanuts and Pistachios. The specific mix of these varieties will depend on several factors:

The amount of fat per serving should not exceed $33\mathrm{.}50$ grams $-$ each serving size is $2$ ounces.

There must be at least $2$ ounces and no more than $7$ ounces of each nut in the mix.

Given the following cost and fat per ounce for each variety, how many ounces of each nut should be used in the new $32-$ounce can to minimize the total cost of each can?

$\backslash$table$[[$Nut Type,Cost Per oz$.($$$),$Fat Per oz$.($g$)],[$Cashews$,$$$0\mathrm{.}45,13],[$Almonds$,$$$0\mathrm{.}30,15],[$Walnuts$,$$$0\mathrm{.}35,18],[$Pecans$,$$$0\mathrm{.}15,20],[$Brazil Nuts,$$0\mathrm{.}30,19],[$Macademia Nuts,$$0\mathrm{.}55,22],[$Peanut$,$$$0\mathrm{.}15,14],[$Pistachios$,$$$0\mathrm{.}60,13]]$