Chapter 5.3, Problem 1P

Explanation of Solution

Calculating the extra payment:

• Let x₁ cars produced daily, x₂ trucks produced daily and m₁ be the daily rent of machine type 1.
• In order to maximize the profit, the following Linear Programming has to be solved:
• max z= $300x_1+400x_2-50m_1$
• Such that,
  • $0.8x_1+x_2-m_1\le 0$
  • $m_1\le 98$
  • $0.6x_1+0.7x_2\le 73$
  • $2x_1+3x_2\le 260$
  • $x_1\ge 88$
  • $x_2\ge 26$
  • $x_1,x_2,m_1\ge 0$
• The output of this Linear Programming is given below:
• max z=$300x_1+400x_2-50m_1$
• Subject to constraint
  • $0.8x_1+x_2-m_1\le 0$
  • $m_1\le 98$
  • $0.6x_1+0.7x_2\le 73$
  • $2x_1+3x_2\le 260$
  • $x_1\ge 88$
  • $x_2\ge 26$
• End
• LP optimum is found at step 3