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

question 306

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, 900 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) \(13 P _ { 1 }\) planes and \(9 P _ { 2 }\) planes
• B) \(5 \mathrm { P } _ { 1 }\) planes and \(22 \mathrm { P } _ { 2 }\) planes
• C) \(14 \mathrm { P } _ { 1 }\) planes and \(7 \mathrm { P } _ { 2 }\) planes
• D) \(9 \mathrm { P } _ { 1 }\) planes and \(13 \mathrm { P } _ { 2 }\) planes

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Definitions:

Allowance for Doubtful Accounts

A contra-asset account used to estimate the amount of accounts receivable that may not be collectible.

Uncollectible Expenses

Costs resulting from customers' failure to pay what they owe, also known as bad debts.

Percent of Sales Method

A financial forecasting model that predicts future variables, such as expenses and inventory levels, as a percentage of projected sales.

Credit Sales

Sales of goods or services that are paid for at a later date, extending credit to customers.