Solve the Linear Programming Problem $\mathrm { P } _ { 1 }$

question 193

Multiple Choice

Solve the linear programming problem.
-An airline with two types of airplanes, $\mathrm { P } _ { 1 }$ and $\mathrm { P } _ { 2 }$ , has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane $P _ { 1 }$ costs $\$ 10,000$ to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane $P _ { 2 }$ costs $\$ 8500$ to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

• A) \(11 \mathrm { P } _ { 1 }\) planes and \(7 \mathrm { P } _ { 2 }\) planes
• B) \(7 \mathrm { P } _ { 1 }\) planes and \(11 \mathrm { P } _ { 2 }\) planes
• C) \(5 \mathrm { P } _ { 1 }\) planes and \(17 \mathrm { P } _ { 2 }\) planes
• D) \(9 \mathrm { P } _ { 1 }\) planes and \(13 \mathrm { P } _ { 2 }\) planes

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Definitions:

Cooperation

The process of working together towards the same end or to accomplish a shared goal.

Structuring

The act of organizing or arranging various elements into a systematic or coherent layout or framework.

Emphasize

To give special importance or prominence to something in speaking or writing.

Ineffective

Describes actions or methods that do not produce the intended result or fail to achieve objectives.