A farmer plans to plant cucumbers and leeks, with a planting area of no more than 50 mu and an investment of 540,000 yuan. What is the output, cost and sales volume of planting cucumbers and leeks in

A farmer plans to plant cucumbers and leeks, with a planting area of no more than 50 mu and an investment of 540,000 yuan. What is the output, cost and sales volume of planting cucumbers and leeks in Foshan? Suppose that the planting area of cucumber and leek is X and Y mu respectively, and the total profit is Z million yuan.

Then the objective function is z = (0.55× 4x-1.2x)+(0.3× 6y-0.9y) = x+0.9y. 。

The linear constraints are x+y≤50 1.2x+0.9y≤54x≥0, and y≥0.

That is, x+y≤504x+3y≤ 180x≥0, y≥0, and the feasible region represented by the inequality group x+y≤504x+3y≤ 180x≥0, y≥0 is made.

It is easy to find points A (0,50), B (30,20) and C (0,45).

Translating the straight line z=x+0.9y, we know that when the straight line z=x+0.9y? When passing through point B (30,20), that is, x=30 and y=20, Z reaches the maximum value, and Zmax=48 (ten thousand yuan).

Therefore, when the planting area of cucumber and leek should be 30 mu and 20 mu respectively, the profit will be the largest.

Therefore, the planting area of cucumber is 30 mu.

So the answer is: 30.