A new Phyto-Pharmaccutical Company named PhytoLife has merged life extension principles from the lost civilizations of Atlantis and Amazonia. Legend has it that the Amnions used the herb Plant-Wert root and lived to be over 100 years old. The dabbled Atlantans used Sea-Fern nodules and lived to be over 100 years as well.
Biological research has shown the active ingredients in these herbs are L-Zortine, an amino acid that promotes cell regeneration, Yarosone, a neurotransmitter that stimulates wellbeing, and Warotase, an enzyme that breaks down oxidizers. The three together are assumed to have given the Atlantans and Amazons their long lives. If a person consumes at least 2400 mg of L-Zortine and 3200 mg of Warotase a day they can expect life extension results similar to those experienced by the Atlantans and the Amazons. Yarosone can be addictive and even fatal if more than 1800 mg are consumed a day.
The local botanist has determined a unit of Plant-blurt root contains 400 mg of L-Zortine, 200 mg of Yarcksone and 600 mg of Warotase. She also determined that Sea-Fern nodules contain 800 mg of Warosone and 400mg of each of the others.
A survey of local farm markets shows that Plant-Wert Root sells for $6 a unit and Sea-Fern Nodules sell for $4.PhytoLife wants to make its product. LiteBeLong for the lowest cost.
a. Write up the standard linear program for PhytoLife.
b. Graph and show PhytoLife's feasible set and a cost line.
c. Using graphical techniques show the most attractive point.
d, Algebraically solve for PhytoLife's formula and its unit costs.