A produce grower is purchasing fertilizer containing three nutrients: A, B, and C. The minimum weekly requirements are 70 units of A, 120 of B, and 210 of C.

Question

A produce grower is purchasing fertilizer containing three nutrients: A, B, and C. The minimum weekly requirements are 70 units of A, 120 of B, and 210 of C. There are two popular blends of fertilizer on the market. Blend 1, costing $3 a bag, contains 2 units of A, 6 of B, and 4 of C. Blend 2, costing $5 a bag, contains 3 units of A, 2 of B, and 10 of C. How many bags of each blend should the grower buy each week to minimize cost of meeting the nutrient requirement?

Answer 1

With the data as originally given the problem is not feasible of being solved, changing the 70 Units of element A to 75 the solution will be 15 and 15 with a minimum value of 120 but I say it again, with the given values the problem is not solvable.

We are here to solve the problems as they come so the answer is that the problem has no solution for the minimum investment.

Answer 2

If you mix blend 1 and blend 2 together, you get a mix with 5 units of A, 8 units of B, and 14 units of C. This mix will cost $8. To get the minimum weekly requirements of 70 units with A, 120 units with B, and 210 units of C, you will need 15 units of both blend 1 and blend 2. This will cost $8 * 15 or $120.

Answer 3

This is basically a linear programming problem.

 

Problem formulation is as follows-----

 

                    Min (3x+5y)

 

Subject to the following constraints----

 

       2x+3y  equal or less than 70

       6x+2y  equal or less than 120

       4x+10y equal or less than 210

 

Graphical approach is to be used.

Plot the objective function and all constraints on a graph.

One of the corner point matching with the objective function gives the solution.