B&K grocery store sells three types of soft drinks: the brand names A1 Cola, A2 Cola, and the cheaper store brand BK Cola. The price per can for A1, A2, and BK are 80, 70, and 60 cents, respectively. On the average, the store sells no more than 500 cans of all colas a day. Although A1 is a recognized brand name, customers tend to buy more A2 and BK because they are cheaper. It is estimated that at least 100 cans of A1 are sold daily and that A2 and BK combined outsell A1 by a margin of at least 4:2.

(a) Show that the optimum solution does not call for selling the A3 brand.

(b) By how much should the price per can of A3 be increased to be sold by the store?

(c) To be competitive with other stores, the store decided to lower the price on all three types of cola by 5 cents per can. Recompute the reduced costs to determine if this promotion will change the current optimum solution.