A Pharmaceutical Company Produces Three Kinds of Cold Formulas: I

A pharmaceutical company produces three kinds of cold formulas: I, II, and III. It takes 5 hr to produce 1,000 bottles of formula I, 4 hr to produce 1,000 bottles of formula II, and 3 hr to produce 1,000 bottles of formula III. The profits for each 1,000 bottles of formula I, formula II, and formula III are $240, $170, and $210, respectively. Suppose, for a certain production run, there are enough ingredients on hand to make at most 7,000 bottles of formula I, 13,000 bottles of formula II, and 6,000 bottles of formula III. Furthermore, suppose the time for the production run is limited to a maximum of 90 hr. How many bottles of each formula should be produced in this production run so that the profit is maximized? What is the maximum profit realizable by the company? Are there any resources left over?

A) 6,000 bottles of formula I, 7,000 bottles of formula II, 9,250 bottles of formula III; maximum profit: $8,631.15; Yes, ingredients for 3,750 bottles of formula III
B) 9,250 bottles of formula I, 6,000 bottles of formula II, 7,000 bottles of formula III; maximum profit: $8,524.95; Yes, ingredients for 3,750 bottles of formula I
C) 7,000 bottles of formula I, 9,250 bottles of formula II, 6,000 bottles of formula III; maximum profit: $4,512.50; Yes, ingredients for 3,750 bottles of formula II
D) 16,250 bottles of formula I, no bottles of formula II, 9,250 bottles of formula III; maximum profit: $6,921.35; Yes, 3 hr of the time for the production run