Question $1$ part a

$15$ points for part $($a$)$

ABCD company is an office equipment company that produces two types of desks: standard and deluxe. Deluxe desks have oak

tops, more expensive hardware and require additional time for finishing and polishing. Standard desks require $80$ square feet of

pine and $10$ hours of labor, while deluxe desks require $60$ square feet of pine, $18$ square feet of oak, and $16$ hours of labor. For the

next week, the company has $5,000$ square feet of pine, $750$ square feet of oak, and $400$ hours of labor available. Standard desks

net a profit of $$150,$ while deluxe desks net a profit of $$320.$ All desks can be sold to national chains shops.

Instructions:

Develop a linear optimization model to determine how many of each type of desk the ABCD company should make next week to

maximize profit contribution $[$Assume: $S=$ units of standard desk produced and $D=$ units of deluxe desk produced. No need to

solve the model, neither graphically nor by Solver: just develop the mathematical model for this part$].$