First of all, it is necessary to arrange for those who are efficient in making coats to make more coats and those who are efficient in making trousers to make more trousers, so as to make the most sets of clothes.
Generally speaking, it is assumed that Group A can sew shirts of a 1 or pants of b 1 every day, and their proportion is that under the condition that Group A makes as many shirts as possible and Group B makes as many pants as possible, the supporting production will be arranged. Suppose that Group A produces X-day jackets and 7-x-day trousers, and Group B produces Y-day jackets and 7-y-day trousers, then the four groups produce 6× 7+8x+9y (pieces) and 1 1× 7+65438 jackets and trousers respectively. According to the meaning of the question, get
42+8x+9y = 77+70- 10x+84- 12y，
Let u = 42+8x+9y, then
Obviously, the larger X is, the larger U is. Therefore, when x=7, the maximum value of U is 125, and the value of Y is 3.
A: Groups A and D were arranged to make jackets in 7 days, while Group C made trousers in 7 days, while Group B made jackets in 3 days and trousers in 4 days, so the number of sets produced was the largest, totaling 125 sets.