Question $12(2\mathrm{.}25$ points$)$

A small company produces three kinds of guitars, traditional, electric and bass, in two factories. Factory A produces $8$ traditional, $5$ electric and $10$ bass guitars in one day, while factory B produces $7$ traditional, $9$ electric and $8$ bass guitars in one day. An order is received for $10$ traditional, $15$ electric and $28$ bass guitars. It costs $$900$ a day fio operate factory A and $$1000$ a day to operate factory $B.$ The manufacturer chooses the number of days to operate each factory in order to minimize cost.

Which of the following inequalities must be satisfied?

$x+y1000$

$10x+8y28$

$x+y+z23$

$7x+10y30$