Answer:
The correct options are 2 and 5.
Step-by-step explanation:
The given table is
Brand A B
Calcium 5 4
Iron 4 6
Vitamins 7 4
Let, x represents the number of spoonfuls of brand A that Steve takes and y represents the number of spoonfuls of brand B that Steve takes.
It is given that Steve needs to take at least 24 milligrams of calcium, 15 milligrams of iron, and 16 milligrams of vitamins.
[tex]5x+4y\geq 24[/tex]
[tex]4x+6y\geq 15[/tex]
[tex]7x+4y\geq 16[/tex]
The points are (1, 4),(1, 5), (2, 3), (3, 2), (4, 1).
Check the above inequalities by each point.
All the above inequality satisfy by points (1,5) and (4,1), because (1,5) and (4,1) lie in the feasible region.
Check the inequalities for (1,5).
[tex]5(1)+4(5)\geq 24\Rightarrow 25\geq 24[/tex]
[tex]4(1)+6(5)\geq 15\Rightarrow 34\geq 15[/tex]
[tex]7(1)+4(5)\geq 16\Rightarrow 27\geq 16[/tex]
All the statements are true.
Check the inequalities for (4,1).
[tex]5(4)+4(1)\geq 24\Rightarrow 24\geq 24[/tex]
[tex]4(4)+6(1)\geq 15\Rightarrow 22\geq 15[/tex]
[tex]7(4)+4(1)\geq 16\Rightarrow 32\geq 16[/tex]
All the statements are true.
Therefore the correct options are 2 and 5.
