B transports 30-x tons to A and 40-(30-x) tons to B = 10+x tons.

0≤x≤30

p = 60x+ 12×5×(50-x)+8×6×(30-x)+ 10×4×( 10+x)

= 60x+3000-60x+ 1440-48x+400+40x

=4840-8x

Because 0≤x≤30

Moreover, P=4840-8x is a linear function, and the larger x is, the smaller p is.

Therefore, when x=30, the minimum freight P =4600 yuan.

At this time, A transports 30 tons to A and 20 tons to B..

B delivers 0 tons to A and 40 tons to B..

2. Company A produces two kinds of products, product A can make a profit in 500 yuan and product B can make a profit in 300 yuan. The company has two workshops, workshop A 120 people and workshop B with 80 people. The total number of people engaged in product A production is planned to be 75, and the total number of people engaged in product B production is planned to be 125. Because of different equipment, or 5 pieces of B products are produced, and workshop B produces 8 pieces of A products or 3 pieces of B products per person every day. How to arrange production to maximize the company's total profit every day?

Solution: If there is a person who produces product A in Party A's workshop, then the person who produces product B has120-a.

There are 75-a people in workshop B to produce product A, and 80-(75-a)=a+5 people to produce product B.

0≤a≤75

Let the profit be p yuan.

p = 500×[6a+8(75-a)]+300×[5( 120-a)+3(a+5)]

= 3000 a+300000-4000 a+ 180000- 1500 a+900 a+4500

=484500- 1600a

This is a linear function. The smaller a is, the greater p is.

Therefore, when a=0, the profit is the largest, and at this time, P = 484,500 yuan.

There are 0 people in production of product A, 0/20 people in production of product B, 75 people in production of product A and 5 people in production of product B..