12. The Furniture City (FC) company makes 3 kinds of couches: (1) Standard, (2) Deluxe, and (3) Luxury styles. Each couch goes through 3 production departments: (1) Cutting and Coloring, (2) Assembly, and (3) Finishing. The total number of hours available each month in each of the above departments is 500, 700 and 400, respectively. The time (in hours) required by 3 departments for making each couch and the profit per couch are listed below. The company has a contract of supplying at least a total of 150 Standard and Luxury couches per month.

Couch	Cutting and Coloring (hrs)	Assembly(hrs)	Finishing(hrs)	Profit ($)
Standard	1	1.8	0.4	200
Deluxe	1.2	2.5	0.7	300
Luxury	1.4	3.5	1	400

The company would like to make a production plan to maximize its total profit.

Define S, D, L as the variables for the numbers of Standard, Deluxe and Luxury couches produced by the company. Then the corresponding LP model is built as follows:

Max 200 S + 300 D + 400 L

Subject to:

1 S + 1.2 D + 1.4 L < 500 (Cutting and Coloring) 1.8 S + 2.5 D + 3.5 L < 700 (Assembly) 0.4 S + 0.7 D + 1 L < 400 (Finishing)

S + L > 150 (contract supply)

All variables are non-negative.

When the above LP model is solved with Excel, we see the following Sensitivity Report.

Adjustable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$B$11	S	150	0	200	16	4
	$C$11	D	172	0	300	1E+30	5.88
	$D$11	L	0	-4	400	4	1E+30
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$B$16	Cutting and Coloring	356.4	0	500	1E+30	143.6
	$B$17	Assembly	700	120	700	299.17	430
	$B$18	Finishing	180.4	0	400	1E+30	219.6
	$B$19	Contract Supply	150	-16	150	238.89	150

At which of the following price point(s) would FC consider producing Luxury couches?

I. $401

II. $409

III. $405

Group of answer choices

a.None of these prices.

b.II or III

c.I or II

d.II only

e.I, II or III

Question 10

The Furniture City (FC) company makes 3 kinds of couches: (1) Standard, (2) Deluxe, and (3) Luxury styles. Each couch goes through 3 production departments: (1) Cutting and Coloring, (2) Assembly, and (3) Finishing. The total number of hours available each month in each of the above departments is 500, 700 and 400, respectively. The time (in hours) required by 3 departments for making each couch and the profit per couch are listed below. The company has a contract of supplying at least a total of 150 Standard and Luxury couches per month.

Couch	Cutting and Coloring (hrs)	Assembly(hrs)	Finishing(hrs)	Profit ($)
Standard	1	1.8	0.4	200
Deluxe	1.2	2.5	0.7	300
Luxury	1.4	3.5	1	400

The company would like to make a production plan to maximize its total profit.

Define S, D, L as the variables for the numbers of Standard, Deluxe and Luxury couches produced by the company. Then the corresponding LP model is built as follows:

Max 200 S + 300 D + 400 L

Subject to:

1 S + 1.2 D + 1.4 L < 500 (Cutting and Coloring) 1.8 S + 2.5 D + 3.5 L < 700 (Assembly) 0.4 S + 0.7 D + 1 L < 400 (Finishing)

S + L > 150 (contract supply)

All variables are non-negative.

When the above LP model is solved with Excel, we see the following Sensitivity Report.

Adjustable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$B$11	S	150	0	200	16	4
	$C$11	D	172	0	300	1E+30	5.88
	$D$11	L	0	-4	400	4	1E+30
Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$B$16	Cutting and Coloring	356.4	0	500	1E+30	143.6
	$B$17	Assembly	700	120	700	299.17	430
	$B$18	Finishing	180.4	0	400	1E+30	219.6
	$B$19	Contract Supply	150	-16	150	238.89	150

Which constraints are binding?

Group of answer choices

Constraints 1 and 3

Constraints 1 and 2

Constraint 3 only

Constraints 2 and 4

Constraints 3 and 4