Princess Peach wants to make a 100 mL fruit smoothie. The smoothie will include at least 10 mL of apples, at least 10 mL of bananas, at least 10 mL of clementines, and at least 10 mL of dewberries. However, for proper taste, she wants to use at least 20 mL more clementines than dewberries, and no more than half of the smoothie can be bananas. The prices in Mushroom Kingdom Mart are as follows: Fruit Price per mL (coins)
Apples 10
Bananas 2
Clementines 5
Dewberries 20
Peach wants to spend as few coins as possible on her smoothie.
A) What are the design variables in this optimization problem?
B) Translate the written description of the problem into a formal optimization problem. Label each expression as an objective function, inequality constraint, equality constraint, or bound on a design variable.
C) Using any strategy you wish, find the values of the design variables that minimize the objective function while satisfying the constraints (i. e. solve the optimization problem). How many coins will the smoothie cost?