*2. B&K grocery store sells three types of soft drinks: the brand names A1 Cola and 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 Al 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 Al 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 B&K. (c) To be competitive with other stores, B&K 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. 5. The Continuing Education Division at the Ozark Community College offers a total of 30 courses each semester. The courses offered are usually of two types: practical, such as woodworking, word processing, and car maintenance, and humanistic, such as history, music, and fine arts. To satisfy the demands of the community, at least 10 courses of each type must be offered each semester. The division estimates that the revenues of offering practical and humanistic courses are approximately $1500 and $1000 per course, respectively. (a) Devise an optimal course offering for the college. (b) Show that the dual price of an additional course is $1500, which is the same as the revenue per practical course. What does this result mean in terms of offering additional courses? (c) How many more courses can be offered while guaranteeing that each will contribute $1500 to the total revenue? (d) Determine the change in revenue resulting from increasing the minimum requirement of humanistics by one course