$(12$pts$)7.$ A coffee shop purchases fresh pastries daily from a baker who sells these pastries by the dozen. Suppose that

the shop's daily budget for pastries is $$960.$ The owner of the coffee shop has estimated the NPV of each type of pastry,

and the maximum amount of each type that should be bought on the basis of space availability and demand. These are

given in the table below.

$(8$ pts$)($a$)$ Which assortment of pastries should the coffee shop choose to buy? $($Calculate the profitability index.$)$

$(4$ pts$)($b$)$ How would your answer change if the daily budget for pastries were $$540$ instead? Explain.