1. the following linear program:

Max 3x₁ + 4x₂

s.t. 2x₁ + 3x₂ < 24

3x₁ + x₂ < 21

x₁, x₂ > 0

Identify the feasible region. (You must draw the feasible region.) (5 points)

Find all the extreme points list the value of x₁ and x₂ at each extreme point. (6 points)

What is the optimal solution? (4 points)

2. Everett Mann's Dream Store sells waterbeds and supplies. The best-selling bed in the store has an annual demand of 400 units. The ordering cost is $40, while the holding cost is $5 per unit per year. There are 250 working days per year, and the lead-time is 6 days.

Develop a total cost model for this system. (4 points)

What is the optimal reorder quantity? (4 points)

What is the cycle time? (4 points)

What is the reorder policy for Everett Mann's Dream Store? (4 points)

What total annual cost does the model give? (4 points)