Solve the given linear programming problem by any suitable method. Maximize: Z=4x+2x2 + 3x3 + 5x4; subject to 2x + 3x2 + 4x3 + 2x = 300, 8x₁ + x2 +x3+5x=300, and x, 20 for j = 1,2,3,4.

A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000