Solve the Following Problem Graphically

question 33

Essay

Solve the following problem graphically: $$\begin{array} { l l } \operatorname { Min } & \mathrm { P } _ { 1 } \left( \mathrm {~d} _ { 1 } ^ { + } \right) + \mathrm { P } _ { 2 } \left( \mathrm {~d} _ { 2 } ^ { - } \right) \\& \\\text {s.t. } & 3 \mathrm { x } _ { 1 } + 5 \mathrm { x } _ { 2 } \leq 45 \\& 3 \mathrm { x } _ { 1 } + 2 \mathrm { x } _ { 2 } - \mathrm { d } _ { 1 } ^ { + } + \mathrm { d } _ { 1 } ^ { - } = 24 \\& \mathrm { x } _ { 1 } + \mathrm { x } _ { 2 } - \mathrm { d } _ { 2 } ^ { + } + \mathrm { d } _ { 2 } ^ { - } = 10 \\& \mathrm { x } _ { 1 } , \mathrm { x } _ { 2 } , \mathrm {~d} _ { 1 } ^ { - } , \mathrm { d } _ { 1 } ^ { + } , \mathrm { d } _ { 2 } ^ { - } , \mathrm { d } _ { 2 } ^ { + } \geq 0\end{array}$$

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Definitions:

Compete

To strive for a goal, such as a prize or higher status, against others by overcoming challenges and obstacles.

Topsoil

The uppermost layer of soil, which has the highest concentration of organic matter and microorganisms, and is where most plant roots grow.

Productivity

The rate at which goods or services are produced, especially in relation to the input of labor, materials, and energy.

Contour Farming

An agricultural technique wherein farming practices are executed following the natural contours of the land, aimed at reducing soil erosion.