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 cost. Coffee Bean type; Arabica, cost per pound 8.00, acidity 8, body 4, Aroma 7. Coffee bean type: Robusta, cost per pound 6.00, acidity 3, body 10, aroma 3. Coffee bean type: Liberica, cost per pound 10.00, acidity 5, body 10, aroma 7. Coffee bean type: Excelsa, Cost per pound 9.00, acidity 6, body 5, aroma 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 these coffee bean proportion should be equal to one pound). Solve using an LP software program or spreadsheet. c. What is the optimal proportion of coffee beans in the signature blend? What is the cost per pound? What are the final characteristics of the signature blend? d. What is the allowable increase or decrease of coffee beans prices that does not require change to the blend proportions? e. Discuss how sensitivity analysis can be used in decision making?