1. A printing company estimates that it will require 1,000 reams of a certain type of paper in a given period. The cost of carrying one unit in inventory for that period is 50 cents. The company buys the paper from a wholesaler in the same town, sending its own truck to pick up the orders at a fixed cost of $20.00 per trip. Treating this cost as the order cost, what is the optimum number of reams to buy at one time? How many times should lots of this size be bought during this period? What is the minimum cost of maintaining inventory on this item for the period? Of this total cost, how much is carrying cost and how much is ordering cost?

**This is an EOQ problem, even though the time period is not a year. All that is required is that the demand value and the carrying cost share the same time reference. This will require approximately 3.5 orders per period. Setup costs and carrying costs are each $70.71, and the annual total is $141.42.**

50

.

0

20

1000

2

=

×

×

=

EOQ

;

2. Given the following data: D=65,000 units per year, S = $120 per setup, P = $5 per unit, and I = 25% per year, calculate the EOQ and calculate annual costs following EOQ behavior.

**EOQ is 3533 units, for a total cost of $4,415.88**

.

3532

5

25

.

120

65000

2

*

=

×

×

×

=

Q

1. A manager must decide on the mix of products to produce for the coming week. Product A requires three minutes per unit for molding, two minutes per unit for painting, and one minute for packing. Product B requires two minutes per unit for molding, four minutes for painting, and three minutes per unit for packing. There will be 600 minutes available for molding, 600 minutes for painting, and 420 minutes for packing. Both products have contributions of $1.50 per unit.

a. Algebraically state the objective and constraints of this problem.

b. Plot the constraints on the grid below and identify the feasible region.

**The objective of the problem is to maximize 1.50A + 1.50B,**

**The constraints are 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420. The plot and feasible region appear in the graph below.**

2. The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420.

a. Plot the constraints on the grid below

c. Identify the feasible region and its corner points. Show your work.

d. What is the optimal product mix for this problem?

**The objective of the problem is to maximize 1.50A + 1.50B,**

**The constraints are 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420. The plot and feasible region appear in the graph below. The corner points are (0, 0), (200, 0), (0, 140), and (150, 75). The first three points can be read from the graph axes. The last corner point is the intersection of the equality 2A + 4B = 600 and 3A + 2B = 600. Multiply the first equality by ½ and subtract from the second, leaving 2A = 300 or A = 150. Substituting A = 150 in either equality yields B = 75.**