please solve these qeustions ***Manually***

course:optmization mathod -non-linear progrramming

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Let xi be binary variable, defined as: equal to 1 if electrical item i is purchased from the mall, 0 otherwise, where i=1,,5. Let a,b,c be non-negative variables, representing kilos of vegetables, meat and cereals respectively, purchased from the mall (i.e, a=100 means that 100kgs of vegetables are purchased from the mall). Note: all the following parts are unrelated. Write the following constraints: (a) If electrical item-1 is not purchased, then electrical item-4 can be purchased. (b) If electrical item-3 is purchased, then cereals cannot be purchased. (c) If electrical item-5 is not purchased, then total weight of vegetables should be above 20kgs. (d) If electrical item-2 is purchased, then total weight of vegetables and cereals cannot exceed 75kgs. (e) If the total weight of vegetables and meat is strictly greater than 80kgs, then electrical item-4 cannot be purchased. (f) The three (vegetables, meat and cereals) cannot be purchased together. Explain the meaning of the following constraints using "if" and "then" style: (h) a+b+c100M(x4) a+b+c22M(x2+x3) (j) x1+x2+x3=1 (k) x2x3 Write each of the following expressions as compactly as possible using summation () and enumeration (v) symbols. (a) x1+4x2+9x3+16x4+25x530 (b) x1,1,1+x1,1,2+x1,1,3+x2,1,1+x2,1,2+x2,1,3a1x1,2,1+x1,2,2+x1,2,3+x2,2,1+x2,2,2+x2,2,3a2 (c) x1+x2+x31x2+x3+x41x3+x4+x51x4+x5+x61x5+x6+x71 (d) x1,11,x1,22,x1,33x2,14,x2,25,x2,36 (e) Hint: For the following part, define matrix A, and wetors b&c max:x1+4x2+1x37x4s.t.:1x11x233x2+3x354x38x442x4+3x12x1,x2,x3,x40