Question

the Natural Fertilizer Company,using the following data. Assume that the company produces 100 pound sacks of 35-20-20 fertilizer for lawns and 100 pound sacks of 14-13-12 fertilizer for gardens, where the numbers are the percentage by weight of nitrate, phosphate, and potash, respectively,in each sack. Assume also that the company has on hand 8 tons of nitrate, 11 tons of phosphate, and7 tons of potash,Assume also that the profit on each sack of lawn fertilizer is $15.00 and the profit on each sack of garden fertilizer is $10.00. How many sacks of each type of fertilizer should the company makein order maximize its profit?When you formulate a linear programming problem to solve this problem,how many variables, how many constraints (both implicit and explicit),and how many objective functions should you have?Number of variables: 2Number of constraints: 5Number of objective functions: 1variable x should be the number of 100 pound bags of lawn fertilizer to be madevariable y should be the number of 100 pound bags of garden fertilizer to be madeFormulate the linear program for this situation.

Answer 1

Answer:

Step-by-step explanation:

Here the number of variables is 2

Variable x should be the number of 100 pound bags of lawn fertilizer to be made.

Variable y should be the number of 100 pound bags of garden fertilizer to be made.

The number of constraints is 5

They are,

0.35x + 0.14y ≤ 160 ----(1)

0.20x + 0.13y ≤ 220 ----(2)

0.20x + 0.12y ≤ 140 ----(3)

x ≥ 0 ----(4)

y  ≥ 0 ----(5)

The number of objective functions is 1

It is, Maximize Z = 15x + 10y