Modeling Analytics

Cover Sheet

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				Homework 2 Solution

Problem 1

Input Parameters
Product Name	Santa's Grotto	Advent Calendar	Fire Station	Princess' Castle	White House	Rose Bouquet	Friendship Boat	Mona Lisa	Race Car	Planet Explorer
Maximum Demand	20000	60000	110000	110000	35000	70000	45000	30000	17000	35000
Selling Price	$55	$35	$80	$80	$65	$45	$65	$75	$150	$50
Material Cost	$15	$8	$30	$30	$23	$10	$30	$10	$45	$20
Molding machine-hours required	0.01	0.002	0.007	0.01	0.01	0.007	0.005	0.003	0.03	0.006
Packing machine-hours required	0.005	0.003	0.01	0.007	0.005	0.006	0.005	0.013	0.025	0.004
	Machine-hours available	Cost per machine-hour
Molding at Plant 1	2000	$500
Packing at Plant 1	2200	$800
Molding at Plant 2	2200	$400
Packing at Plant 2	1700	$650
Decisions
	Santa's Grotto	Advent Calendar	Fire Station	Princess' Castle	White House	Rose Bouquet	Friendship Boat	Mona Lisa	Race Car	Planet Explorer
Production Quantity at Plant 1	7609	0	110000	0	0	70000	45000	21304	0	35000
Production Quantity at Plant 2	12391	60000	0	110000	35000	0	0	8696	16000	0
Objective
Profit	$ 18,932,500	To be filled in
Constraints
	Santa's Grotto	Advent Calendar	Fire Station	Princess' Castle	White House	Rose Bouquet	Friendship Boat	Mona Lisa	Race Car	Planet Explorer
Total Production Quantity	20000	60000	110000	110000	35000	70000	45000	30000	16000	35000
<= Max demand	20000	60000	110000	110000	35000	70000	45000	30000	17000	35000
	Machine-hours used	<= Machine-hours available
Molding at Plant 1	1835	2000
Packing at Plant 1	2200	2200
Molding at Plant 2	2200	2200
Packing at Plant 2	1700	1700
Margin Calculations
	Santa's Grotto	Advent Calendar	Fire Station	Princess' Castle	White House	Rose Bouquet	Friendship Boat	Mona Lisa	Race Car	Planet Explorer
Selling Price	$55	$35	$80	$80	$65	$45	$65	$75	$150	$50
Material Cost	$15	$8	$30	$30	$23	$10	$30	$10	$45	$20
Molding Machine-Hour Cost (Plant 1)	$5.00	$1.00	$3.50	$5.00	$5.00	$3.50	$2.50	$1.50	$15.00	$3.00
Packing Machine-Hour Cost (Plant 1)	$4.00	$2.40	$8.00	$5.60	$4.00	$4.80	$4.00	$10.40	$20.00	$3.20
Molding Machine-Hour Cost (Plant 2)	$4.00	$0.80	$2.80	$4.00	$4.00	$2.80	$2.00	$1.20	$12.00	$2.40
Packing Machine-Hour Cost (Plant 2)	$3.25	$1.95	$6.50	$4.55	$3.25	$3.90	$3.25	$8.45	$16.25	$2.60
Margin per Unit at Plant 1	$31.00	$23.60	$38.50	$39.40	$33.00	$26.70	$28.50	$53.10	$70.00	$23.80
Margin per Unit at Plant 2	$32.75	$24.25	$40.70	$41.45	$34.75	$28.30	$29.75	$55.35	$76.75	$25.00

#25, pg.125

Chemical manufacturing
	Process 1	Process 2
Cost per hour	$400	$100
Output production per hour
	Process 1	Process 2	Chemical produced		Chemical required
Chemical A	300	100	1100	>=	1000
Chemical B	100	100	500	>=	500
Chemical C	100	0	300	>=	300
	Process 1	Process 2
Hours run	3	2
Total cost	$1,400

This model is trickier than it looks. The decision variable cells are not how much of the chemical to produce; they are the hours of each process to run. Once the latter are known, the amounts of the chemicals produced are known. Note from the graph that the first constraint (shown in blue) is redundant, that is, it will always be satisfied if the other two constraints are satisfied.

#26, pg.125

Manufacturing desks and chairs
Inputs
	Desks	Chairs
Unit margins	$250	$145
Wood usage per unit	4	3
Decisions
	Desks	Chairs
Units produced	125	500
Constraint on wood
	Wood used		Wood available
	2000	<=	2000
Constraint on chairs
	Chairs produced		Chairs required
	500	>=	500
Objective to maximize
Profit	$103,750

Problem 2.2