Three Plants P1, P2, and P3 of a Gas Corporation

question 55

Essay

Three plants P1, P2, and P3 of a gas corporation supply gasoline to three of their distributors in the city located at A, B, and C locations. The plants' daily capacities are 4500, 3000, and 5000, gallons respectively, while the distributors' daily requirements are 5500, 2500, and 4200 gallons. The per-gallon transportation costs (in $) are provided in the table below.
​ $$\begin{array}{l}\begin{array} { l c c c } &\text { Distributor }\\\hline \text { Plant } & \text { A } & \text { B } & \text { C } \\\hline \text { P1 } & 0.8 & 0.5 & 1 \\\text { P2 } & 0.7 & 0.65 & 0.8 \\\text { P3 } & 0.5 & 0.45 & 0.7\end{array}\end{array}$$ ​
Because of a failure of expected supply earlier, the distributors this time have decided to charge a penalty of $0.45, $0.55, and $0.5 per gallon, respectively for the locations A, B, and C to avoid any further delays.
Find an alternative optimal solution for this transportation problem?

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Definitions:

Teratogens

Agents or factors that can cause malformation or defects in the developing embryo or fetus.

Blastocyst

An early stage of embryonic development characterized by a fluid-filled structure that, after implantation in the uterus, develops into the embryo and placenta.

Endoderm

The innermost layer of cells or tissue of an embryo in early development, which gives rise to the lining of the digestive and respiratory systems.

Maternal Stress

Psychological and physiological stress experienced by a mother during pregnancy, which can affect fetal development and child outcomes.