A baby food company produces both cereal and juice. Each serving of the cereal provides 60 calories and 10 grams of carbohydrates but no vitamin C, while each serving of the juice provides 60 calories, 15 grams of carbohydrates, and 120% of the daily allowance of Vitamin C. Each day, you want to provide your baby with at least 120 calories, at least 25 carbohydrates, and at least 100% of the daily allowance of Vitamin C. The cereal costs $0.10 per serving and the juice costs $0.30 per serving. How many servings of cereal and how many servings of juice should you give your child each day in order to meet all of your nutritional requirements while minimizing cost? (You can give fractions of servings.) In particular:

a) Identify the unknowns and label your variables. (For example, x = the amount of carbohydrates or something like that.) Furthermore, identify the objective function and the constraints, and write down the equations/inequalities that they correspond to. show your work if needed please.

b) Sketch the feasible region. Show your work please step by step.

c) Finish the problem: Use your work in parts (a) to (c) and do some more work to determine the number of servings of cereal and the number of servings of juice that you should give your child each day in order to meet all of your nutritional requirements while minimizing cost. (You can give fractions of servings.) Show your work please step by step.