Chapter 5.3, Problem 4P

Explanation of Solution

Calculating the extra payment:

• Let x_mn is the number of units of product n at plant m.
• In order to minimize the cost of meeting these demands, the following Linear Programming has to be solved:
• min z= $5x_{11}+6x_{12}+8x_{13}+8x_{21}+7x_{22}+10x_{23}$
• Such that,
  • $x_{11}+x_{12}+x_{13}\le 10,000$
  • $x_{21}+x_{22}+x_{23}\le 10,000$
  • $x_{11}+x_{21}\ge 6,000$
  • $x_{12}+x_{22}\ge 8,000$
  • $x_{13}+x_{23}\ge 5,000$
  • All variables ≥ 0
• The output of this Linear Programming is given below:
• min z= $5x_{11}+6x_{12}+8x_{13}+8x_{21}+7x_{22}+10x_{23}$
• Subject to constraint
  • $x_{11}+x_{12}+x_{13}\le 10,000$
  • $x_{21}+x_{22}+x_{23}\le 10,000$
  • $x_{11}+x_{21}\ge 6,000$
  • $x_{12}+x_{22}\ge 8,000$
  • $x_{13}+x_{23}\ge 5,000$
• End
• LP optimum is found at step 2