A Company Makes Two Types of Telephone Answering Machines: the Standard

A company makes two types of telephone answering machines: the standard model and the deluxe model. Each machine passes through three processes: $P _ { 1 } ,$ $P _ { 2 }$ and $P _ { 3 }.$ One standard answering machine requires 1 hour in $P _ { 1 } ,$ 4 hours in $P _ { 2 },$ and 3 hours in $P _ { 3 }.$ One deluxe answering machine requires 3 hours in $P _ { 1 } ,$ 5 hours in $P _ { 2 },$ and 1 hour in $P _ { 3 }.$ Because of employee work schedules, $P _ { 1 }$ is available for 24 hours, $P _ { 2 }$ is available for 47 hours, and $P _ { 3 }$ is available for 27 hours. If the profit is $22 for each standard model and $23 for each deluxe model, how many units of each type should the company produce to maximize profit?

A) 8 standard models and 3 deluxe models
B) 9 standard models and 0 deluxe models
C) 8 standard models and 0 deluxe models
D) 0 standard models and 8 deluxe models
E) 3 standard models and 7 deluxe models