Pacific-Gulf Oil Company Is Faced with the Problem of Refining

Pacific-Gulf Oil Company is faced with the problem of refining three petroleum components into regular and premium gasoline in order to maximize profit. Components 1 and 2 are pooled in a single storage tank and component 3 has its own storage tank. Regular and premium gasolines are made from blending the pooled components and component 3. Prices per gallon for the two products and three components, as well as product specifications, are listed below. $$\begin{array} { l c } & \text { Price Per Gallon } \\\text { Regular gasoline } & \$ 2.80 \\\text { Fremium gasoline } & 3.10 \\\text { Component 1 } & 2.40 \\\text { Component 2 } & 2.50 \\\text { Component 3 } & 2.75\end{array}$$ $$\begin{array} { c c } \text { Product } & \text { Specifications } \\ \text { Regular gasoline }& \text { At most } 25 \% \text { component } 1 \\& \text { At least } 40 \% \text { component } 2 \\ & \text { At most 30\% component 3 } \\\text { Premium gasoline }& \text { At least 30\% component 1 } \\& \text { At most } 50 \% \text { component 2 } \\& \text { At least } 25 \% \text { component 3 }\end{array}$$ The maximum number of gallons available for each of the three components is 4000, 8000, and 8000, respectively. Formulate a nonlinear program to determine: 1) what percentages of component 1 and component 2 should be used in the pooled mixture, and 2) how to make regular and premium gasoline by blending the mixture of components 1 and 2 from the pooling tank with component 3.