Homework:Hw 07_QM B_LinearProg

Question 10, Problem B.24 (additional/static)

Part 12 of 12

HW Score: 58.18%, 16.29 of 28 points

Points: 0 of 7

Save

Question content area

Part 1

Mann Enterprises is a Houston manufacturer of tables and accessories for personal computers. The company is caught in a vicious cross fire between rapidly dropping market prices from competitors worldwide for its products and stable domestic costs for its materials. The 15 different products noted below must be scheduled to maximize profits or there will be no jobs and no firm in another 3 months. Your job as the new OM graduate is to address the issues raised this morning by Laura Mann, the president, in an emergency meeting in her office. Without being told so explicitly, you conclude that if you don't get the schedule done accurately and in a timely manner, you will be history. To your relief, the industrial engineers and accountants have provided the data shown below. The issues, as recorded in your notes, are indented in (a) through (f).

Product	Steel Alloy Required (Lb.)	Plastic Required (Sq. Ft.)	Wood Required (Bd. Ft.)	Aluminum Required (Lb.)	Formica Required (Bd. Ft.)	Labor Required (Hr.)	Minimum Monthly Demand (Units)	Contribution to Profit
A158		0.4	0.7	5.8	10.9	3.1		$18.79
B179	4	0.5	1.8	10.3	2.0	1.0	20	6.31
C023	6		1.5	1.1	2.3	1.2	10	8.19
D045	10	0.4	2.0			4.8	10	45.88
E388	12	1.2	1.2	8.1	4.9	5.5		63.00
F422		1.4	1.5	7.1	10.0	0.8	20	4.10
G366	10	1.4	7.0	6.2	11.1	9.1	10	81.15
H600	5	1.0	5.0	7.3	12.4	4.8	20	50.06
I701	1	0.4		10.0	5.2	1.9	50	12.79
J802	1	0.3		11.0	6.1	1.4	20	15.88
K900		0.2		12.5	7.7	1.0	20	17.91
L901	2	1.8	1.5	13.1	5.0	5.1	10	49.99
M050		2.7	5.0		2.1	3.1	20	24.00
N150	10	1.1	5.8			7.7	10	88.88
P259	10		6.2	15.0	1.0	6.6	10	77.01
Availability per month	980	400	600	2,500	1,800	1,000

Part 2

Specify the objective function and constraints for the problem.

Let	Xi = monthly production quantity of a product beginning with letter i.

Objective function (round your responses to two decimal places):

Maximize Z =

18.79XA + 6.31XB + 8.19XC + 45.88XD + 63.00XE + 4.10XF + 81.15XG + 50.06XH + 12.79XI + 15.88XJ + 17.9117.91XK + 49.9949.99XL + 2424XM + 88.8888.88XN + 77.0177.01XP

Part 3

Constraints (enter your responses as whole numbers):

Material constraints:
Steel Alloy (C1)		4XB + 6XC + 10XD + 12XE + 10XG + 5XH + XI + XJ + 2XL + 10XN + 10XP less than or equals 980980
Plastic (C2)		.4XA + .5XB + .4XD + 1.2XE + 1.4XF + 1.4XG + 1.0XH + .4XI + .3XJ + .2XK + 1.8XL + 2.7XM + 1.1XN less than or equals 400400
Wood (C3)		.7XA + 1.8XB + 1.5XC + 2.0XD + 1.2XE + 1.5XF + 7.0XG + 5.0XH + 1.5XL + 5.0XM + 5.8XN + 6.2XP less than or equals 600600
Aluminum (C4)		5.8XA + 10.3XB + 1.1XC + 8.1XE + 7.1XF + 6.2XG + 7.3XH + 10.0XI + 11.0XJ + 12.5XK + 13.1XL + 15.0XP less than or equals 25002500
Formica (C5)		10.9XA + 2.0XB + 2.3XC + 4.9XE + 10.0XF + 11.1XG + 12.4XH + 5.2XI + 6.1XJ + 7.7XK + 5.0XL + 2.1XM + 1.0XP less than or equals 18001800
Labor constraint (C6):		3.1XA + 1.0XB + 1.2XC + 4.8XD + 5.5XE + .8XF + 9.1XG + 4.8XH + 1.9XI + 1.4XJ + 1.0XK + 5.1XL + 3.1XM + 7.7XN + 6.6XP less than or equals 10001000
Minimum demand
constraints:		(C7): XA0	(C8): XB20	(C9): XC10
		(C10): XD10	(C11): XE0	(C12): XF20
		(C13): XG10	(C14): XH20	(C15): XI50
		(C16): XJ20	(C17): XK20	(C18): XL 10
		(C19): XM greater than or equals 2020	(C20): XN greater than or equals 1010	(C21): XP greater than or equals 1010

Part 4

A linear programming software shows the following solution:

LOADING...

Click the icon to view the data concerning products.

LOADING...

Click the icon to view the data concerning constraints.

Part 5

a) Only product

A158

is not produced.

Part 6

b) Clearly explain the meaning of each shadow price.

Since the shadow price for constraints

C2,

C5,

C6,

C7,

C11,

C18,

and

C20

is 0, these are

nonbinding

constraints.

Part 7

The shadow price for constraint

C1

is $2.71, which is the benefit of

increasing

the right-hand side by one unit.

Part 8

The shadow price for constraint

C19

is $29.24, which is the benefit of

reducing

the right-hand side by one unit.

Part 9

c) A number of workers interested in saving money for holidays have offered to work overtime next month at a rate of $12.50 per hour. What should the response of management be?

The workers should work

00

hours per month overtime (enter your response as a whole number).

Part 10

d) Two tons of steel alloy are available from the overstocked supplier at a local cost of $8,000.

The steel

should

be purchased.

Part 11

If 44 pounds of it are purchased, the total profit will increase by

$119.32119.32

(round your response to two decimal places).

Part 12

e) The accountants have just discovered that an error was made in the contribution to profit for product N150. The correct value is actually $8.88.

The

objective function

should be corrected.

Part 13

The corrected objective function is (round your responses to two decimal places):

Maximize Z =

18.79XA + 6.31XB + 8.19XC + 45.88XD + 63.00XE + 4.10XF + 81.15XG + 50.06XH + 12.79XI + 15.88XJ + 17.9117.91XK + 49.9949.99XL + 2424XM + 8.888.88XN + 77.0177.01XP

1) Management is considering the abandonment of five product lines (those beginning with letters A through E). If no minimum monthly demand is established, the new minimum demand constraints will be enter your responses as whole numbers): V V ) (C7): XAS (C10): XD (C13): XG 2 10 (C16): Xj2 20 (C19): XM220 (Cg): XB (C11) XE (C14): XH 2 20 (C17): XK 220 (C20): XN2 10 (Co): Xc (C12): XF (C15): X/2 50 (C18): XL 210 (C21): Xp 2 10