A garden superstore sells 4 kinds of fertilizer from 20 pallet spaces aligned along a fence.

Weekly demands for the 4 fertilizers are 20, 14, 9, and 5 pallets, respectively, and each pallet holds 10 bags. The sales counter is at the beginning of the fence, and every bag sold must be carried from its pallet to the counter. Whenever all pallets for a product are empty, the space allocated for that fertilizer is refilled completely using a fork truck from secondary storage.

Store managers need to decide how many pallet spaces to assign each product to minimize both the number of times per week such refilling will be necessary and the total carrying distance of bags sold. Each fertilizer will have at least one pallet space.

(a) Assuming that fractional numbers of pallet spaces are allowed, briefly explain how this pallet allocation problem can be modeled by the multiobjective nonlinear program min 20>x1 + 14>x2 + 9>x3 + 5>x4 min 2001x1>22 + 1401x1 + x2>22

+ 901x1 + x2 + x3>22

+ 501x1 + x2 + x3 + x4>22 s.t. a 4

i = 1 xj = 20 xj Ú 1, j = 1,c, 4

(b) and

(c) as in Exercise 8-1.