Your company produces a health drink that requires blending three different ingredients: X$,$ Y$,$ and Z$.$ Each ingredient has a cost associated with it$,$ and the final product must satisfy certain percentage requirements for nutrients such as protein, carbohydrates, and vitamins. Ingredient X costs $$8$ per unit, with $30\%$ protein, $40\%$ carbohydrates and $5\%$ vitamins; Ingredient Y costs $$5$ per unit, with $10\%$ protein, $30\%$ carbohydrates and $15\%$ vitamins; Ingredient Z costs $$10$ per unit, with $20\%$ protein, $45\%$ carbohydrates and $25\%$ vitamins;It is required that the final product must contain at least $20\%$ protein, at least $30\%$ carbohydrates, and at least $15\%$ vitamins. Additionally, the overall volume of the final product must be at least $200$ units. Assume that there is no shrinkage or expansion issue.Define your variable and build your linear program model to determine a recipe with the least total cost.