In preparation for Easter, Hershey and Mondelez are looking to make variety packages of sweet and sour candy assortments and promote them as part of their Egg Hunt promotion. They want the candy package to be a blend of fun-sized packages of SourPatch Kids, individually wrapped Jolly Rancher hard candies, and Twizzlers Cherry candy bite packs. Information about these three components is provided on the table:

Ingredient	Cost	Weight	Sugar Content Grams	Calories
Sour Patch Kids	.32	5 oz.	19	150
Jolly Ranchers	.12	1 oz.	11	30
Twizzlers	.26	3 oz.	13	110

Formulate a linear programming model to determine the optimal number of units of each item to include in the mix. The variety bag will be labeled 50 ounces so they want to make sure to include at least 50 ounces of candy. The blend should contain no more than 4000 calories and no more than 450 grams of sugar. Jolly Ranchers should be no more than 45% of the units in the variety pack and SourPatch Kids fun packs should be at least 20% of the candy mixture. Develop a linear programming model that meets these restrictions and minimizes the cost of the blend.

Formulate the linear programming problem only. Be sure to define decision variables, provide objective function, and all constraints. DO NOT SOLVE.