Acandidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. two types of ads will be used: radio and television. each radio ad costs $200 and reaches an estimated 3,000 people. each television ad costs $500 and reaches an estimated 7,000 people. in planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. also, the number of radio ads must be at least as great as the number of television ads. how many ads of each type should be used? how many people will this reach? let x1= the number of radio ads purchasedx2= the number of television ads purchasedmaximize3,000x1+7,000x2(ma ximize exposure)subject to: 200x1+500x2≤40,000(budget constraint)x1≥10(at least 10 radio ads purchased)x2≥10(at least 10 television ads purchased)x1≥x2(# of radio ads ≥ # of television ads)x1, x2≥0(non-negativity constraints)

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