Answer:
The correct options are 2 and 4.
Step-by-step explanation:
Let x be the number o men's shirts and y be the number of women's shirts.
Cost of men’s shirts = $8
Cost of women’s shirts = $12
Luis can spend up to $240 buying men’s and women’s shirts for his club.
[tex]8x+12y\leq 240[/tex] ..... (1)
He needs to buy at least 3 of each type of shirt.
[tex]x\geq 3,y\geq 3[/tex] .... (2)
The women’s shirts must be at least twice the number of men’s shirts.
[tex]y\geq 2x[/tex] .... (3)
Check all the given options whether they satisfy all the above inequalities or not.
In option 1, (7,17).
[tex]8(7)+12(17)\leq 240[/tex]
[tex]260\leq 240[/tex]
This statement is false. Therefore (7,17) is not a possible solution.
In option 2, (6,15).
[tex]8(6)+12(15)\leq 240[/tex]
[tex]228\leq 240[/tex]
This statement is true.
[tex]6\geq 3,15\geq 3[/tex]
This statement is true.
[tex]15\geq 2(6)[/tex]
[tex]15\geq 12[/tex]
This statement is also true. Therefore (6,15) is a possible solution.
In option 3, (5,8)
Check this point for inequality (3).
[tex]8\geq 2(5)[/tex]
[tex]8\geq 10[/tex]
This statement is false. Therefore (5,8) is not a possible solution.
In option 4, (4,9).
[tex]8(4)+12(9)\leq 240[/tex]
[tex]140\leq 240[/tex]
This statement is true.
[tex]4\geq 3,9\geq 3[/tex]
This statement is true.
[tex]9\geq 2(4)[/tex]
[tex]9\geq 8[/tex]
This statement is also true. Therefore (4,9) is a possible solution.
From the below graph it is clear that the points (6,15) and (4,9) lie on the feasible region.
Therefore, the correct options are 2 and 4.
