Exhibit 7.4 The Following Questions Are Based on the Problem Below

question 37

Essay

Exhibit 7.4
The following questions are based on the problem below.
Robert Gardner runs a small, local-only delivery service. His fleet consists of three smaller panel trucks. He recently accepted a contract to deliver 12 shipping boxes of goods for delivery to 12 different customers. The box weights are: 210, 160, 320, 90, 110, 70, 410, 260, 170, 240, 80 and 180 for boxes 1 through 12, respectively. Since each truck differs each truck has different load capacities as given below: Robert would like each truck equally loaded, both in terms of number of boxes and in terms of total weight, while minimizing his shipping costs. Assume a cost of $50 per item for trucks carrying extra boxes and $0.10 per pound cost for trucks carrying less weight.
The following integer goal programming formulation applies to his problem.
Y₁ = weight loaded in truck 1; Y₂ = weight loaded in truck 2; Y₃ = weight loaded in truck 3;
X_i,j = 0 if truck i not loaded with box j; 1 if truck i loaded with box j. Given the following spreadsheet solution of this integer goal programming formulation, answer the following questions.
-Refer to Exhibit 7.4. Given the solution indicated in the spreadsheet, which trucks, if any, are under an equal weight amount, and which trucks are over an equal weight amount?

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Definitions:

Retained Earnings

The accumulated net income of a company that is retained and reinvested in the business rather than paid out as dividends.

Service Revenue

Income earned by a company for providing services rather than selling physical goods.

Equipment

Equipment consists of the fixed assets a company uses in its operational activities to produce goods or provide services, not intended for sale.

Prepaid Insurance

An asset account that represents insurance payments made in advance, which are to be expensed over the period the insurance coverage pertains to.