Discuss the below in detail:
Q: Perfect Stack builds two types of wooden palettes: standard and extra long. The palettes are assembled from three components: standard separators, extra long separators, and cross pieces. Each standard palette consists of 3 standard separators and 5 cross pieces, and takes 0.25 hours to assemble. Each extra long palette consists of 4 extra long separators and 7 cross pieces, and takes 0.40 hours to assemble. The components need to be fabricated before being used to assemble a palette: it takes 0.22 hours to fabricate a standard separator, 0.28 hours to fabricate an extra long separator, and 0.20 hours to fabricate a cross piece. Perfect Stack has 5 hours of assembly time and 8 hours of fabrication time available. Standard palettes are sold at a profit of $6 each, and extra long palettes are sold at a profit of $9 each. Assume all palettes produced are sold. Assume that fractional solutions are acceptable.
Write a linear program that determines a production plan for Perfect Stack that maximizes profit.
Use the following decision variables: x1 = number of standard palettes assembled and sold, x2 = number of extra long palettes assembled and sold, y1 = number of standard separators fabricated, y2 = number of extra long separators fabricated, y3 = number of cross pieces fabricated.