Solve the 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 $\mathrm { P } _ { 1 }$ 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) $9 \mathrm { P } _ { 1 }$ planes and $13 \mathrm { P } _ { 2 }$ planes
B) $7 \mathrm { P } _ { 1 }$ planes and $11 \mathrm { P } _ { 2 }$ planes
C) $11 \mathrm { P } _ { 1 }$ planes and $7 \mathrm { P } _ { 2 }$ planes
D) $5 \mathrm { P } _ { 1 }$ planes and $17 \mathrm { P } _ { 2 }$ planes

Question

Quizplus · Accepted Answer

To solve this problem, we can set up inequalities based on the requirements and solve them using linear programming or by evaluating the options given. The goal is to minimize the cost while meeting or exceeding the passenger requirements for each class. By evaluating the options given:- Option A: $9 \mathrm { P } _ { 1 }$ planes can carry $9 \times 20 = 180$ first class, $9 \times 50 = 450$ tourist class, and $9 \times 110 = 990$ economy class passengers. $13 \mathrm { P } _ { 2 }$ planes can carry $13 \times 18 = 234$ first class, $13 \times 30 = 390$ tourist class, and $13 \times 44 = 572$ economy class passengers. Combined, they can carry $414$ first class, $840$ tourist class, and $1562$ economy class passengers, meeting the requirements.The other options either do not meet the passenger requirements or are not as cost-effective when calculated similarly.

Solve the Problem P1\mathrm { P } _ { 1 }P1​

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