2. (10 points) Suppose we have a problem as follows:

A manager is determining how many tables and how many chairs to produce so as to maximize the total profit. He has collected data as in the table below.

A linear program is formulated for this problem Max 70X₁ + 50X₂ (objective function)

S.T. 4X₁ + 3X₂ <= 240 (constraint 1)

2X₁ + X₂ <= 100 (constraint 2)

X₁, X₂ >= 0

in which X₁ = number of tables to produce,

X₂ = number of chairs to produce.

Answer the following questions (2.1) to (2.5) which are about the above linear program:

(2.1) There is a term 70X₁ in the objective function. What does that term 70X₁ mean? (select one)

a. 70X₁.

b. Profit per table.

c. Profit per chair.

d. Total profit of X₁ tables.

e. Total profit of X₁ chairs.

e. Total profit of 70 tables.

f. Total profit of 70 chairs.

(2.2) There is a term 2X₁ in Constraint 2. What does that term 2X₁ mean? (select one)

b. Total carpentry hours needed for 2 tables.

c. Total painting hours needed for 2 tables.

d. 2 carpentry hours are needed for X₁ tables.

e. 2 painting hours are needed for X₁ chairs.

f. Total carpentry hours needed for X₁ tables.

g. Total painting hours needed for X₁ tables.

h. Total painting hours available.

(2.3) The left-hand-side of constraint 2 is 2X₁+X₂. What does that (2X₁+X₂) mean? (select one)

a. Total carpentry hours available.

b. Total painting hours available.

c. Total carpentry hours to be used.

d. Total painting hours to be used.

e. Total profit.

(2.4) In the linear program, _____________ represents total carpentry hours available. (select one)

a. 70X₁

b. 50X₂

c. 70X₁+50X₂

d. 4X₁

e. 3X₂

f. 4X₁+3X₂

g. 2X₁

h. X₂

i. 2X₁+X₂

j. 240

k. 100

(2.5) Given a solution (X₁=25, X₂=30), how many carpentry hours to be used associated with the solution? (Show you calculations)