Find the Complete Optimal Solution to This Linear Programming Problem

question 34

Essay

Find the complete optimal solution to this linear programming problem.
$$\begin{array} { l l } \text { Min } & 3 x + 3 y \\\text { s.t. } & 12 x + 4 y \geq 48 \\& 10 x + 5 y \geq 50 \\& 4 x + 8 y \geq 32 \\& x , y \geq 0\end{array}$$

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Definitions:

Subsidy

A financial contribution provided by government to reduce the cost of producing goods or services and support businesses or consumers.

External Costs

Costs of an economic activity that are not borne by the parties directly involved in the transaction but by other individuals or society at large.

Supply Curve

A graph that represents the relationship between the price of a good and the quantity of the good that suppliers are willing to offer for sale.

Socially Optimal

A condition that maximizes societal welfare, often referring to the optimal distribution of resources and goods.