Question

A farmer can buy two types of plant​ food, mix A and mix B. Each cubic yard of mix A contains 35 pounds of phosphoric​ acid, 15 pounds of​ nitrogen, and 16 pounds of potash. Each cubic yard of mix B contains 14 pounds of phosphoric​ acid, 18 pounds of​ nitrogen, and 64 pounds of potash. The minimum monthly requirements are 840 pounds of phosphoric​ acid, 540 pounds of​ nitrogen, and 768 pounds of potash. If x is the number of cubic yards of mix A used and y is the number of cubic yards of mix B​ used, write a system of linear inequalities that indicates appropriate restraints on x and y. Find the set of feasible solutions graphically for the amounts of mix A and mix B that can be used.

Answer 1

Answer:

The answer is below

Step-by-step explanation:

Given that the minimum monthly requirements are 840 pounds of phosphoric​ acid, hence:

35 pounds of phosphoric acid mix A + 14 pounds of phosphoric acid mix B ≥ 840 pounds of phosphoric​ acid

35x + 14y ≥ 840

The minimum monthly requirements are 540 pounds of nitrogen, hence:

15 pounds of nitrogen mix A + 18 pounds of nitrogen mix B ≥ 540 pounds of nitrogen

15x + 18y ≥ 540

The minimum monthly requirements are 768 pounds of potash, hence:

16 pounds of potash mix A + 64 pounds of potash mix B ≥ 768 pounds of potash

16x + 64y ≥ 768

Also, x ≥ 0 and y ≥0.

Therefore the equations are:

35x + 14y ≥ 840

15x + 18y ≥ 540

16x + 64y ≥ 768

x ≥ 0 and y ≥ 0

Plotting with geogebra gives the graph below.

The point are (0,60), (48,0), (18,15), (32,4)