4. [20 points] A coffee shop chain is considering blending four different types of coffee beans to create a new signature blend that meets specific taste and cost requirements. The goal is to determine the optimal proportion of the four coffee beans that provide the desired flavor profile at the lowest possible cost. Coffee Bean Type Cost per pound ($) Characteristics per pound Acidity Body Aroma Arabica 8.00 8 4 7 Robusta 6.00 3 10 3 Liberica 10.00 5 10 7 Excelsa 9.00 6 5 5 The coffee shop owner has decided that the signature blend must have a minimum acidity of 5 units, minimum body of 7 units, and minimum aroma of 6 units. The signature blend must contain at least 10% Arabica beans. Robusta and Liberica beans cannot exceed 66% (combined) of the total weight. a. Formulate as an LP problem to find the optimal blend. State the decision variables, objective function, and constraints. (Hint: In the blend, the total weight of each coffee bean proportion should be equal to one pound.) b. Solve using an LP software program or spreadsheet. Show all the work. c. What is the optimal proportion of coffee beans in the signature blend