I will answer step by step:
1) "The client wants no more than 250 roses in vases" and "The smaller vase will contain 6 roses and the larger vase will contain 10 roses". If x represents the number of small vases and y represent the number of large vases, this mathematically means:
[tex]6x+10y\leq250[/tex]
2) "The client requires that there are at least twice as many small vases as large vases"
[tex]x=2y[/tex]
3) The client requires that there are at least 8 small vases and no more than 14 large vases.
[tex]x\ge8[/tex][tex]y\leq14[/tex]
That is all the options that are correct!