Subject - Optimization

6. For each of the following LPs, express the optimal value and the optimal solution in terms of the problem parameters (c,k,d,,d1,d2,). If the optimal solution is not unique, it is sufficient to give one optimal solution. Do any 5 of the following 11 . The rest are optional. (a) minimizesubjecttocTx0x1 The variable is xRn. (b) minimizesubjecttocTx1x1 The variable is xRn. (c) minimizesubjecttocTx11Tx1 The variable is xRn. (d) minimizesubjecttocTx1Tx=1,x0 The variable is xRn. maximizesubjecttoeTx1Tx=k,0x1. The variable is xRn,k is an integer with 1kn. (f) maximizesubjecttocTx1Txk,0x1 The variable is xRn.k is an integer with 1kn. (g) maximizesubjecttocTxdTx=,0x1. The variable is xRn, and the components of d are positive. (h) minimizesubjecttoeTx0x1x2xn1 The variable is xRn. (i) maximizesubjecttocTxyxy,1Ty=k,y1. The variables are xRn and yRn.k is an integer with 1kn. (j) minimizesubjectto1Tu+1Tvuv=c,u0,v0 The variables are uRn and vRn. (k) minimizesubjecttod1Tud2Tvuv=c,u0,v0. The variables are uRn and vRn. We assume that d1d2