s02rec03

# s02rec03 - carrying charge of \$25. Furthermore, unsatisfied...

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Recitation 3 Problems 15.053 Introduction to Optimization February 22, 2002 1. Fernwood Labor (More practice on formulations) Fernwood Lumber produces plywood. The cost to produce 1000 board feet of plywood varies from month to month because of the variation in handling costs, energy consumption, and raw materials costs. The production cost per 1000 board feet in each of the next 6 months is: Month 1 2 3 4 5 6 Production cost (\$) 900 950 1250 1050 900 850 Demand in 1000’s of board feet for the next 6 months is as follows: Month 1 2 3 4 5 6 Total Demand 60 70 110 80 70 60 450 Fernwood can produce up to 90,000 board feet per month. It also has the option of carrying inventory from one month to the next for a carrying cost of \$25 per 1000 board feet per month. For example, 1000 board feet produced in month 1 for demand in month 2 incurs a
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Unformatted text preview: carrying charge of \$25. Furthermore, unsatisfied demand in one month can be filled in later periods at the cost of \$40 per 1000 board feet per month-delay. Fernwood would like to know how much to produce each month and how much inventory to carry in order to satisfy demand at minimum cost. Formulate a linear program. 2. BHM #4, p. 84 Maximize z = x 1 s.t.-x 1 + x 2 &lt;= 2 x 1 + x 2 &lt;= 8-x 1 + x 2 &gt;= -4 x 1 &gt;= 0, x 2 &gt;= 0 a) State the above in canonical form b) Solve by the simplex method 3. BHM #12a, p. 87 (with some modification) Solve the following problem using the 2 phases of the simplex method: Max x 4 s.t. x 1 6x 2 + x 3 x 4 = 5- 2x 2 + 2x 3 3x 4 &gt;= 3 3x 1 2x 3 + 4x 4 =-1 x 1 &gt;= 0, x 3 &gt;= 0, x 4 &lt;= 0...
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