(* Discounts and Over-Declared Shipments *)



Clear[demand, setup, holding, price, totalCost];

demand = 7000; setup = 20; holding = 0.36; weight = 3.8;

price = PWSFreeze[PWS[

        {{{1, IB[750]}, 6.21 &},

          {{750, IB[1125]}, 5.94 &},

          {{1125, IB[2250]}, 5.88 &},

          {{2250, Infinity}, 5.76 &}}]];



breakpoints = {weight, 216.5, 500, 1000, 2000, 5000, 10000, 20000, Infinity}/

      weight;

rates = {30.30, 24.92, 18.87, 15.39, 10.67, 8.87, 6.58};

rates = (rates weight/100) /. r_?NumberQ -> (r # &);

rates = Prepend[rates, 65.60 &];



x = Transpose[{Rest[Reverse[breakpoints]], Reverse[rates]}];

tariff = {{Take[breakpoints, -2], Last[rates]}};

cost[{qty_, rate_}] := rate[qty];

Clear[q];

While[

    z = cost[x[[1]]];(* cost to beat *)

    q0 = IB[x[[1, 1]]];

    x = Select[Rest[x], cost[#] < z &];

    x != {},

    w = First[q /. Solve[x[[1, 2]][q] == z, q]];

    tariff = Join[{{{x[[1, 1]], IB[w]}, x[[1, 2]]},

          {{w, q0}, Evaluate[z] &}}, tariff]];

If[breakpoints[[1]] < q0, 

    PrependTo[tariff, {{breakpoints[[1]], q0}, Evaluate[z] &}]];

tariff = PWSFreeze[PWS[tariff]];

Plot[tariff[q], {q, 1, 7000}, AxesLabel -> {"Quantity", "Shipping Cost"}];



purchase = demand setup/# & + demand price + (holding #/2 &) price;

totalCost = purchase + (demand/# &) tariff;

Plot[totalCost[q], {q, 1, 6000}, PlotRange -> {44000, 56000}];

tC = totalCost /. Infinity -> 99999;

FindMinimum[tC[q], {q}]