This question is based on the following model:

A firm has ten outlets that must be supplied with a certain product. The demands ( all positive) at the outlets are d₁ ,d_{2 .....},d₁₀, and these demands must be exactly satisfied ( i.e., d_i units must be distributed to outlet i). The firm may supply these demands by having a supplier deliver directly to each outlet. The supplier charges $50 for each unit delivered, independent of the outlet location. The supplier would charge on $35 per unit for any location if the location would order at least D UNITS. Since each of the d_j <D, the firm can make no use of the discount. The firm is considering leasing a centrally located warehouse for K>0 dollars and using this warehouse as an intermediary depot. The depot could order any quantity and could distribute to any number of outlets. It has been agreed that the depot would pay the same as the outlets ($50 per unit if <D units are ordered; $35 per unit if the total order is at least D units).

The cost of sending a unit from the warehouse to outlet i is C_i > 0, i= 1, 2, ,10 .

Assume that D< , i.e., the amount to qualify for the discount is less than the sum of the 10 individual demands.

Management would like to know:

1) Should the warehouse be leased?

2) If so, which outlets should be served by the warehouse and which should be supplied directly by the supplier?

In formulating a model to answer these questions, let

X_i=quantity sent directly from supplier to location i

Y_i = quantity sent from warehouse to location i

Z = quantity sent from supplier to warehouse

A correct set of constraints for this model is x_i + y_i = d_i, i = 1,2,.10

ztD

z t

x_i ,y_i 0 (i=1,2,10); z0;

t=0 or 1

For the model as stated, there will never be an optimal solution in which the depot orders a positive amount that is less than D units.

options:

	True
	False