Chapter 4, Problem 12RP

Explanation of Solution

Optimal solution:

• Given table:

Product	Labor	Lumber	Paint	Price ($)	Variable Cost ($)
1	1.5	2	3	26	10
2	3	3	2	28	6
3	2	4	2	31	7

• Let,
  • x₁ = Number of product I produced
  • x₂ = Number of product II produced
  • x₃ = Number of product III produced
  • x₄ = Amount of additional labor purchased
  • x₅ = Amount of additional paint purchased
  • x₆ = Amount of additional lumber purchased
  • x₇ = Amount of labor, lumber, and paint required for producing product I
  • x₈ = Amount of labor, lumber, and paint required for producing product II
  • x₉ = Amount of labor, lumber, and paint required for producing product III
  • (d₁)^- = Underachievement in obtaining a profit of at least $10500
  • (d₁)⁺ = Overachievement in obtaining a profit of at least $10500
  • (d₂)^- = Underachievement in purchasing no additional labor
  • (d₂)⁺  = Overachievement in purchasing no additional labor
  • (d₃)^- = Underachievement in purchasing no additional paint
  • (d₃)⁺ = Overachievement in purchasing no additional paint
  • (d₄)^- =Underachievement in purchasing no additional lumber
  • (d₄)⁺ = Overachievement in purchasing no additional lumber
...