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.

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)

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐