Integer programming There is an integer programming to solve the offline version of the ski-rental problem. ■Ve introduce some variables x,zi,z2,.,zk∈ {0,1}. x:indicate whether we eventually buy it. zi:indicate whether we rent on day i. IP: min B·x+=1Z1 s.t.x+z1≥1， j∈[k] x,Z∈{0,1 j∈[k] 8Integer programming ◼ There is an integer programming to solve the offline version of the ski-rental problem. ◼ We introduce some variables 𝑥, 𝑧1 , 𝑧2 ,… , 𝑧𝑘 ∈ 0,1 . ❑ 𝑥: indicate whether we eventually buy it. ❑ 𝑧𝑖 : indicate whether we rent on day 𝑖. ◼ IP: min 𝐵 ⋅ 𝑥 + σ𝑗=1 𝑘 𝑧𝑗 𝑠.𝑡. 𝑥 + 𝑧𝑗 ≥ 1, ∀𝑗 ∈ 𝑘 𝑥, 𝑧𝑗 ∈ 0,1 ∀𝑗 ∈ 𝑘 8