Exam 5: Integer Programming

You have been asked to select at least 3 out of 7 possible sites for oil exploration. Designate each site as S1, S2, S3, S4, S5, S6, and S7. The restrictions are: Restriction 1. Evaluating sites S1 and S3 will prevent you from exploring site S7. Restriction 2. Evaluating sites S2 or S4 will prevent you from assessing site S5. Restriction 3. Of all the sites, at least 3 should be assessed. Assuming that Si is a binary variable, write the constraint for the third restriction.

In a mixed integer model, the solution values of the decision variables are 0 or 1.

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation cost and to possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and are choosing between facilities with capacities of 5 or 10 million. The fixed costs of each facility as well as the cost of shipping between regions is shown in the table below. The decision variables are defined as follows: Xij = quantity shipped from supply region i to demand region j. i = 1, 2, 3, 4 and j = 1, 2, 3, 4. Yik = 1 if facility k is selected for supply region i; 0 otherwise, where i = 1, 2, 3, 4 for each supply region; k = 1 (low capacity facility) or 2 (high capacity facility) -Max Z = 5x1 + 6x2 Subject to17x1 + 8x2 ? 136     3x1 + 4x2 ? 36     X1, x2 ? 0 and integer What is the optimal solution?

Which of the following is not an integer linear programming problem?

An optimal solution to an integer programming problem is ensured by rounding down non-integer solution values.

The Exorbitant Course Fees. The $75 per credit hour course fee tacked on to all the MBA classes has generated a windfall of $56,250 in its first semester. "Now we just need to make sure we spend it all," the Assistant Dean cackled. She charged the Graduate Curriculum Committee with generating a shopping list before their next meeting. Four months later, the chairman of the committee distributed the following. As the professor for the quantitative modeling course, he tended to think in terms of decision variables, so he added the left-most column for ease of use. Decision Variable Item Cost Note A iPads for everybody \ 750/ unit Must get a cover if these are purchased B iPad covers with MBA logo \ 25/ unit Not needed unless we buy iPads C Speaker series \ 15,000 Can't afford both this and the iPads D Subscriptions to the Wall Street Joumal \ 10/ unit Don't need if we have the electronic version Subscriptions to the electronic version of the Wall E Street Joumal \5 /unit Worthless without the iPads -Which of the constraints best describes the relationship between the iPads for everyone and the speaker series?

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same. Machine Fixed Cost to Setup Production Run Variable Cost per Hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 -Write a constraint to ensure that if machine 4 is used and machine 1 will not be used.