the marketing club at your college has decided to raise funds by selling three types of t-shirt: one with a single-color "ordinary" design, one with a two-color "fancy" design, and one with a three-color "very fancy" design. the club feels that it can sell up to 330 t-shirts. "ordinary" t-shirts will cost the club $6 each, "fancy" t-shirts $8 each, and "very fancy" t-shirts $10 each, and the club has a total purchasing budget of $3,400. it will sell "ordinary" t-shirts at a profit of $2 each, "fancy" t-shirts at a profit of $6 each, and "very fancy" t-shirts at a profit of $4 each. how many of each kind of t-shirt should the club order to maximize profit? hint [see example 3.]
"ordinary" t-shirt(s)
"fancy" t-shirt(s)
"very fancy" t-shirt(s)
what is the maximum profit the club can make?
$

Asystem of linear equations with more equations than unknowns is sometimes called an overdetermined system. can such a system be consistent? illustrate your answer with a specific system of three equations in two unknowns. choose the correct answer below. a. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 6 b. no, overdetermined systems cannot be consistent because there are fewer free variables than equations. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 12 c. yes, overdetermined systems can be consistent. for example, the system of equations below is consistent because it has the solution nothing. (type an ordered pair.) x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 8 d. no, overdetermined systems cannot be consistent because there are no free variables. for example, the system of equations below has no solution. x 1 equals 2 comma x 2 equals 4 comma x 1 plus x 2 equals 24