A company produces two types of products, Product A and Product B$.$ Product A requires $2$ labor hours and $3$ units of raw material, while Product B requires $1$ labor hour and $2$ units of raw material. The company has $100$ labor hours and $90$ units of raw material available. The profit per unit for Product A is $$30,$ and for Product B is $$20.$ Assume that the company produces X$1$ units of product A and X$2$ units of product $2.$ Which of the following represents the correct objective for this product mix problem?

Question $1$ Answer

a$.$

$2$X$1+$X$2=100$

b$.$

$30$X$1+10$X$2=100$

c$.$

Maximize$(30$X$1+20$X$2)$

d$.$

$30$X$1+2$X$2=190$