EM 605 HW 1
3.4-10 part a
Answer:
Let the 𝑋𝑖𝑗 as the amount of the space leased and i is in the i month and the j is a period
of j months. (i=1,2,3,4,5 and j=1,2,3,…,6-i)The object would be minimize total cost of
leasing while satisfying all space weekly requirement. So objective function would be
Minimize C = 650(𝑋11 + 𝑋21 + 𝑋31 + 𝑋41 + 𝑋51) + 1000(𝑋12 + 𝑋22+ 𝑋32 +𝑋42)
+1350(𝑋13 + 𝑋23 + 𝑋33) + 1600(𝑋14 + 𝑋24) + 1900𝑋15
subject to 𝑋11 + 𝑋12 + 𝑋13 + 𝑋14 + 𝑋15 ≥ 30, 000
𝑋12 + 𝑋13 + 𝑋14 + 𝑋15 + 𝑋21 + 𝑋22 + 𝑋23 + 𝑋24 ≥ 20, 000
𝑋13 + 𝑋14 + 𝑋15 + 𝑋22 + 𝑋23 + 𝑋24 + 𝑋31 + 𝑋32 +𝑋33 ≥ 40,
000
𝑋14 + 𝑋15 + 𝑋23 + 𝑋24 + 𝑋32 + 𝑋33 + 𝑋41 + 𝑋42 ≥ 10, 000
𝑋15 + 𝑋24 + 𝑋33 + 𝑋42 + 𝑋51 ≥ 50, 000
and 𝑋𝑖𝑗≥ 0, for i = 1, …, 5 and j = 1, …, 6 − i.
3.4-14 part a
