The following table shows the unit price and the minimum quantity at which suppliers j = 1

c, 5 have to bid to supply State University

(SU) with office desk chairs. SU wishes to find the lowest total cost combination of purchases that will procure at least the minimums from each supplier used, and will obtain a total of at least 400 chairs.

Supplier 1 2 3 4 5 Unit Price 200 400 325 295 260 Min Quantity 500 50 100 100 250

(a) Although SU must obviously buy integer numbers of chairs from each supplier, explain why it makes sense to model the number of chairs purchased from each supplier as a nonnegative, continuous variable.

Also indicate what issues are left that make the problem discrete.

(b) Using nonnegative continuous xj for the number of chairs purchased from supplier j, and whatever other decision variables are required, formulate SU’s problem as a Mixed-Integer Linear Program. Be sure to define any additional decision variables and annotate each objective function and constraint with its meaning.

11-16. Focus Inc. wants to consolidate its camera manufacturing operations at 2 of the current 4 plants. At the same time, each surviving plant will begin full 3-shift operations running 168 hours per week. The following table shows the estimated cost

(in $ million) of moving operations from each current plant to each other, along with the projected number of production hours per week the moved operation would add at the new site. For example, closing operation 1 and moving it to site 3 would cost

$320 million and add 70 hours per week at site 3.

To Site From Site 1 5 Omaha 2 5 Denver 3 5 Muncie 4 5 Kent l = Omaha Cost 0 450 320 550 Hours 56 56 70 56 2 = Denver Cost 770 0 640 690 Hours 82 82 70 70 3 = Muncie Cost 810 770 0 660 Hours 40 40 60 60 4 = Kent Cost 580 610 490 0 Hours 56 56 56 56 Formulate Focus Inc.’s problem of choosing which two sites to retain and how to move the others to minimize total moving cost as an Integer Linear Program. Use decision variables xij = 1 of plant i is moved to site j and = 0 otherwise, so that xii = 1 means the plant will be retained. Be sure to annotate objectives and constraints to indicate their meaning.