Linear Programming

I want to solve these questions for my company: a governmental planning agency wishes to determine the sources of purchase of fuel for use by n depots from among m bidders. Suppose that the maximum quantity offer by bidder i is a, gallons and the demand of depot j is A governmental planning agency wishes to determine the sources of purchase of fuel for use by n depots from among m bidders. Suppose that the maximum quantity offered by bidder i is ai gallons and that the demand of depot j is bj gallons. Let Cij be the unit delivery cost for bidder i to the jth depot. A) formulate the problem of minimizing the total purchasing cost as a linear program. b)Suppose that a discount in the unit delivery cost is offered by bidder i if the ordered quantity exceeds the level ai. How would you incorporate this modification in the model developed in part (a) ? Q5 suppose that the following linear programming has a solution x^*: Min cx s.t. Ax ≥b,x≥0 write the dual of this problem and explain why there is exists a solution u^* to the dual. Suppose that the cost vector is tripled in the linear program, that is c is replaced by 3c in the formulation above. For this modifies problem give solutions to both the primal and the dual