A marketing research firm would like to survey undergraduate and graduate college students about whether or not they take out student loans for their education. There are different cost implications for the region of the country where the college is located and the type of degree. The survey cost table is provided below:

Student type

Region

undergraduate

graduate

East

$$10$

$$15$

Central

$$12$

$$18$

West

$$15$

$$21$

The requirements for the survey are as follows:

The survey must have at least $1500$ students

At least $400$ graduate students

At least $100$ graduate students should be from the West

No more than $500$ undergraduate students should be from the East

At least $75$ graduate students should be from the Central region

At least $300$ students should be from the West

The marketing research firm would like to minimize the cost of the survey while meeting the requirements. Let X$1=$ # of undergraduate students from the East region, X$2=$ # of graduate students from the East region, X$3=$ # of undergraduate students from the Central region, X$4=$ # of graduate students from the Central region, X$5=$ # of undergraduate students from the West region, and X$6=$ # of graduate students from the West region.According to this problem, the constraint that there must be at least $400$ graduate students is expressed as:

Select one:

a$.$

X$1+$ X$2+$ X$3+$ X$4+$ X$5+$ X$6<=400.$

b$.$

X$1+$ X$2+$ X$3+$ X$4+$ X$5+$ X$6>=400.$

c$.$

X$2+$ X$4+$ X$6>=400.$

d$.$

X$1+$ X$3+$ X$5>=400.$