Question

farmer has to plant two kinds of trees,say A and B on a land with a 4400 square meter area.Each A tree requires 25 sq m of land, and B requires 40 Sq m of land. The annual water reuirement of tree A is 30 units and that of B is15 units, while at most 3300 units water is available. It is esmtimate that the ratio of the number of B trees to the number of A trees should not be less than 6/19 and not more than 17/8. The return from one B tree $50,while from one A tree is one and a half times that of return from B, fomulate the plantation poject of the farmer in terms of linear programming problem so that the return is maximum.

Answer 1

Answer:

Two kinds of tree A and B

Land -> 25A + 40B <_ 4400

Water -> 30A + 15B <_ 3300

Ratio -> 6/19 <_ B/A <_ 17/8

Max z = (3/2 x 50)A + 50B

Max z = 75A + 50B

at (40,85)

Z = 75 (40) + 50 (85)

= 7250

at (80,60)

Z = 75 (80) + 50 (60)

= 9000

AT (95,30)

Z = 75 (95) + 50 (30)

= 8625

Max value is $900 at A = $95 AND B = $30