Given this linear programming model, solve the model and then answer the questions that follow.

Maximize	12x1 + 18x2+ 15x3	where x1 = the quantity of product 1 to make etc.
Subject to

Machine	5x1	+	4x2	+	3x3		160	minutes
Labor	4x1	+	10x2	+	4x3		288	hours
Materials	2x1	+	2x2	+	4x3		200	pounds
Product 2					x2		16	units
			x1, x2, x3				0

a-1. Are any constraints binding?

• Yes

• No

a-2. If so, which one(s)?

• Machine and materials

• Machine and labor

• Materials

• Labor

• None

b-1. If the profit on product 3 was changed to $22 a unit, what would the values of the decision variables be?

• The decision variables would change

• The decision variables would not change

b-2. What would the new value of the objective function be? The objective function value Z = c-1. If the profit on product 1 was changed to $22 a unit, what would the values of the decision variables be?

• The decision variables will not change

• The decision variables will change

c-2. What would the new value of the objective function be?

• There is no change in objective function value

• There is change in objective function value

d-1. If 10 hours less of labor time were available, what would the values of the decision variables be?

• The decision variables will not change

• The decision variables will change

d-2. What would the new value of the objective function be?

• The objective function value will not change

• The objective function value will change

e. If the manager decided that as many as 20 units of product 2 could be produced (instead of 16), how much additional profit would be generated?

• None

• Any change in profit

f-1. If profit per unit on each product increased by $1, would the optimal values of the decision variables change?

• Yes

• No

f-2. What would the optimal value of the objective function be? (Omit the "$" sign in your response.) The objective function value Z =