The Hickory Cabinet and Furniture Co$.$ produces sofas, tables, and chairs at its plant in Greensboro, North Carolina. The plant uses three main resources to make furniture; wood, upholstery and labor. The resource requirements for each piece of furniture and total resources available weekly are as follows:

Resource Requirements

Wood $($ft$.)$

Upholstery $($yrd$.)$

Labor $($hr$.)$

Sofa

$7$

$12$

$6$

Table

$5$

$-$

$9$

Chair

$4$

$7$

$5$

Total available

Resources

$2250$

$1000$

$240$

The furniture is produced on a weekly basis and stored in a warehouse until the end of the week, when it is shipped out. The warehouse has a total capacity of $650$ pieces of furniture. Each sofa earns $$400$ in profit, each table $$275,$ and each chair, $$190.$ Also the company has a contract with a distributor to provide at least $50$ units of sofa, and can sell only a maximum of $150$ units of chairs. Additionally, number of tables produced has to be at least twice as many as the number of sofas produced. The company wants to know how many pieces of each type of furniture to make per week to maximize profit.

Which of the following choices is the correct objective function for this problem

Your answer:

Max. Z $=2250$x$1+1000$x$2+240$x$3$

Max. Z $=400$x$1+275$x$2+190$x$3$

Max. Z $=7$x$1+12$x$2+6$x$3$

Max. Z $=4$x$1+7$x$2+5$x$3$