Question $1$

$5$ pts

Use the following problem statement to answer questions $1-3.$

A company produces a drug from two ingredients. Each ingredient contains the same three antibiotics in different proportions. One gram of ingredient $1$ contributes $3$ units of antibiotic $1,$ and one gram of ingredient $2$ contributes $1$ unit of antibiotic $1.$ The drug requires at most $18$ units of antibiotic $1.$ At least $6$ units of antibiotic $2$ are required, and the ingredients each contribute $1$ unit per gram. At least $14$ units of antibiotic $3$ are required; a gram of ingredient $1$ contributes $2$ units, and a gram of ingredient $2$ contributes $6$ units. The cost for a gram of ingredient $2$ is $$80,$ and the cost for a gram of ingredient $1$ is $$50.$ The company wants to formulate a linear programming model to determine the number of grams of each ingredient that must go into the drug in order to meet the antibiotic requirements at the minimum cost.

$[$Note: $x_1=$ the number of grams of ingredient $1.x_2=$ the number of grams of ingredient $2]$

Which of the following objective functions is correct?

MinZ$=501+802$

MinZ$=31+x2$

MinZ$=801+502$

Question $2$

$5$ pts

Which of the following constraints is correct?

$21+6214$

$x1+x214$

Question $3$

$5$ pts

Which of the following constraints is correct?

$x_1+x_{2}6$

$61+621$