4. Let xij = 1 if students from district i are sent to school j
xij = 0 otherwise
Then the appropriate IP is
Min z = 110x11 + 220x12 + 37.5x21 + 127.5x22 + 80x31 + 80x32
+ 117x41 + 36x42 + 135x51 + 54x52
s.t. 110x11 + 75x21 + 100x31 + 90x41 + 90x51150
a. Let xij = number of tons of steel j produced at plant i. Then the
supply at plant 1 is 40(60)/20 = 120 tons, the supply at plant 2 is
40(60)/16 = 150 tons, and the supply at plant 3 is 40(60)/15 = 160
tons. We obtain the following balanced t
6a. x1 is non-basic so changing the coefficient of x 1 in the objective
function will only change the coefficient of x 1 in the optimal row 0.
Let the new coefficient of x1 in the objective function be 3 + . The
new coefficient of x1 in the optimal row 0
Hints for solving HW#5
I am addressing several points that you guys should pay attention to:
1. The majority of you made a mistake in Cycling problem.
Why? You started pivoting from (-9) in the column where x2 locates,
because you took two rows as a tie.
Problem 1 (from the textbook) 108(5).
We assume the following order of events ensues each month.
Short-term loan and interest on short and long-term loans are paid. We assume
first interest payments on the January
Solution to HW3
Let PTi = Part-time people starting at i PM and FTi = Full-time
people starting at hour i . Also define INVi = checks that have
arrived before hour i and are unprocessed at time i, and Pi =
checks processed between time i and time i
a. We want to make x1 larger and x2 smaller so we move down and to the right.
b. We want to make x1 smaller and x2 larger so we move up and to left.
c. We want to make both x1 and x2 smaller so we move down and to left.
The LP is