The integer programming problem below has been developed to help First National Bank decide where, out of 10 possible sites, to locate four new branch offices:

Xi represents Winter Park, Maitland, Osceola, Downtown, South Orlando, Airport, Winter Garden, Apopka, Lake Mary, and Cocoa Beach, for i equals 1 to 10, respectively.

(a) Where should the four new sites be located, and what will be the expected return?

(b) If at least one new branch must be opened in Maitland or Osceola, will this change the answers? Add the new constraint and rerun.

(c) The expected return at Apopka was overestimated.

The correct value is $160,000 per year

(i.e., 160). Using the original assumptions—that is, ignoring part (b)—does your answer to part

(a) change?

IP for Problem 10-32 Maximize expected returns = 120X100X2 +110X3 +140X4 +155X5 +128X6 + 145X7+ 190X8 + 170X9 + 150X10 subject to 20X130X220X3 + 25X4 + 30X5 + 15X + 5X2 + 20X320X45X5 + 30X6 + 25X7 +20X8 +25X9 + 30X10 110 5X6 + 10X7 + 20X8 + 5X9 +20X10 50 X+ X6 + X7 + X + X10 3 X2 + X+ X5 + X8 + X9 = 2 X + X3 + X10 1 X + X2 + X3 + X4 + X5 + X6 + X7 + X8 + X9 + X10 4 All X; = 0 or 1