5 (18 3 pts) Suppose X 1 and X 2 are defined as X 1 number of mugs to produce, X 2 number of cups to produce Answer the following questions with X 1 and X 2 defined as above (5 1) (2 pts) If a mug can generate $4 5 of profit, and a cup can generate $3 4 of profit, then what is the expression representing the total profit of X 1 mugs and X 2 cups (5 2) (2 pts) If a mug needs 2 pounds of clay and a cup needs 1 5 pounds of clay, then what is the expression representing total pounds of clay to be used for producing X 1 mugs (5 3) (2 pts) Write out an expression representing total number of mugs and cups to be produced in terms of X 1 and X 2 (5 4) (3 pts) Suppose a mug needs 2 pounds of clay and a cup needs 1 5 pounds of clay, and there are 600 pounds of clay available Use a constraint to represent the total pounds of clay to be used should be no more than the clay available (5 5) (3 pts) Use a constraint in X 1 and X 2 to represent No more than 200 mugs will be produced (5 6) (3 pts) Use a constraint in X 1 and X 2 to represent At least 50 cups must be produced (5 7) (3 pts) Use a constraint in X 1 and X 2 to represent Number of cups should be no less than number of mugs (5 8) (3 bonus pts) Use a constraint in X 1 and X 2 to represent for each mug produced, at least 2 cups must be produced

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5 . (18 +3 pts) Suppose X 1 and X 2 are defined as: X 1 =number of mugs to produce, X 2 =number of

5. (18⁺³ pts) Suppose X₁ and X₂ are defined as:

X₁=number of mugs to produce,

X₂=number of cups to produce.

Answer the following questions with X₁ and X₂ defined as above:

(5.1) (2 pts) If a mug can generate $4.5 of profit, and a cup can generate $3.4 of profit, then what is the expression representing "the total profit of X₁ mugs and X₂ cups"?

(5.2) (2 pts) If a mug needs 2 pounds of clay and a cup needs 1.5 pounds of clay, then what is the expression representing "total pounds of clay to be used for producing X₁ mugs"?

(5.3) (2 pts) Write out an expression representing "total number of mugs and cups to be produced" in terms of X₁ and X₂.

(5.4) (3 pts) Suppose a mug needs 2 pounds of clay and a cup needs 1.5 pounds of clay, and there are 600 pounds of clay available.Use a constraint to represent "the total pounds of clay to be used should be no more than the clay available".

(5.5) (3 pts) Use a constraint in X₁ and X₂ to represent "No more than 200 mugs will be produced."

(5.6) (3 pts) Use a constraint in X₁ and X₂ to represent "At least 50 cups must be produced".

(5.7) (3 pts) Use a constraint in X₁ and X₂ to represent "Number of cups should be no less than number of mugs".

(5.8) (3 bonus pts) Use a constraint in X₁ and X₂ to represent "for each mug produced, at least 2 cups must be produced".