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 changed to $22 a unit, would the decision variables' values change?

• Yes

• No

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

c-1. If the profit on product 1 changed to $22 a unit, would the decision variables' values change?

• Yes

• No

c-2. Will the objective function value change, based on the change in c-1?

• Yes

• No

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

• Yes

• No

d-2. Will the objective function value change, based on the change in c-1?

• Yes

• No

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?

• $0

• $4

• $16

• $72

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 be the new value of the objective function?