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Suppose that the problem in Exercise 10 is the continuous relaxation of an integer programming problem (i.e., the same problem but with the restriction that the variables take integral values). Suppose further that the best known integral solution has value 8. Derive two inequalities from the dual solution that can be propagated to reduce domains. Also, derive an upper bound on the non-basic variable x3 from its reduced cost. (You can deduce the reduced cost from the slack in the corresponding dual constraint. Why?)Exercise 10
Consider the linear programming problem
min 4x1+4x2+3x3x1+2x2+x3>=22x1+x2+x3>=3x1,x2,x3>=0
Solve the classical dual by hand and use the solution to obtain the surrogate that provides the tightest bound on the optimal value of the primal.
What is the optimal value? (There is no need to solve the primal directly.) Now use complementary slackness to find an optimal solution of the primal by solving two simultaneous equations.
Briarcrest Condiments is a spice-making firm. Recently, it developed a new process for producing spices. The process requires new machinery that would cost $2,224,349.
At Jarvie's current shop, Bad Dog Cycles, each employee is allowed to purchase four bicycles a year at a discount. Bad Dog has an average gross profit percentage on bicycles of 25 percent.
The housekeeping departmenent at ricardo clinic, a multispecialty practice in Corpus christi had 152318.00 in direct cost during last year. These costs must be allocated to three revenue producing patient serices departments using the direct meth..
Patterson, Inc. receives a $16,000 payment two years in advance of delivering a completed novel. A five percent interest rate applies. Prepare the journal entries which Patterson, Inc. would record for the cash receipt and revenue recognition.
Write (2.40) for each release time t1 and each deadline t2 (t1 2) in the problem of Table 2.11. Verify that (2.41) are the non-redundant inequalities.
Write the knapsack cuts that correspond to the non-maximal packings I = {1}, {2}, {3}, {4} for constraint (2.3a).
A number of overweight Americans filed a class action suit for deceptive trade practices and negligence against McDonald's Corporation, the fast-food chain famous for its hamburgers, French fries, and chicken nuggets.
McDermott estimates that the new project will generate $900,000 in annual sales at the end of each of the next four years and that operating costs (excluding depreciation) will equal $400,000.
a project has annual cash flows (including the intial year) of -140,000, 30,000, 60,000, 40,000, 30,000 and 30,000. caculate the NVP for this project if the discount rate is 12%
Bill makes annual deposits of $1900 to an an IRA earning 8% compounded annually for 20 years. At the end of the 20 years Bill retires. a) What was the value of his IRA at the end of 20 years
Suppose In a Found Ltd. just issued a dividend of $1.73 per share on its common stock. The company paid dividends of $1.40, $1.47, $1.54, and $1.65 per share in the last four years.
Assume that this high correlation is expected to continue. Your forecasting staff has indicated that the Swiss franc may exhibit minor appreciation over the next few months, but depreciation is unlikely.
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