Question

Profit/bracelet

Profit/necklace

A

44

66

Saleem

B

32

16

A jeweler can make necklaces and bracelets from

C

42

19

gold and silver. Demand for bracelets is no more

D

81

81

than four. Available ounces of gold are

36

E

16

32

Available ounces of silver are

10

Each bracelet takes

4

oz. of gold and

2

oz. of silver.

Each necklace takes

6

oz. of gold and

1

oz. of silver.

Bracelets

Gold in

Silver in

Bracelets

Necklaces

Gold in

Silver in

Necklace

Extra

Extra

Max

#Made

Bracelets

Bracelets

Profit

#Made

Necklaces

Necklaces

Profit

Gold

Silver

Profit

A

B

C

D

E

For each profit scenario, how would things change if you had one more ounce of gold?

For each profit scenario, how would things change if you had one more ounce of silver?

For each profit scenario, how would things change if demand could be as high as 5 bracelets?

For each profit scenario, how would things change if profit/bracelet increased by one?, decreased by one?

For each profit scenario, how would things change if profit/necklace increased by one?, decreased by one?

Answer 1

Let us start with scenario A,

Set Objective: Bracelet Necklace To: Max OMin O Value Of: Nos. Profit Subject to 44 66 İ-SUMPRODUCT(SC-3:SD$3.C4:D4LI Ry Changing Variable Cells: SCS3:SDS3 Gold Silver Bracelet damand 1 SUMPRODUCT(SC$3:SD$3,C6:D6) 36 SUMPRODUCT(SC$3:SD$3,C7:D7) 10 SUMPRODUCT(SC$3:$D$3,C8:D8)4 Subject to the Constraints: SES6:SES8 <SGS6:SGS8 Change Delete 12 13 Reset All 15 16 17 18 Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: SimplexLP Options

	Bracelets Made	Gold in bracelet	Silver in bracelet	Bracelets Profit	Necklaces Made	Gold in necklace	Silver in necklace	Necklace Profit	Extra Gold	Extra Silver	Max Profit
A	0	0	0	0	6	36	6	396	0	4	396
B	4	16	8	128	2	12	2	32	8	0	160
C	4	16	8	168	2	12	2	38	8	0	206
D	3	12	6	243	4	24	4	324	0	0	567
E	0	0	0	0	6	36	6	192	0	4	192

For each profit scenario, how would things change if you had one more ounce of gold?

	Dual price of Gold constraint (from the sensitivity reports)	Increase in profit
A	11	11
B	0	No change
C	0	No change
D	10.125	10.125
E	5.333	5.333

For each profit scenario, how would things change if you had one more ounce of silver?

	Dual price of Silver constraint (from the sensitivity report)	Increase in profit
A	0	No change
B	16	16
C	19	19
D	20.25	20.25
E	0	No change

For each profit scenario, how would things change if demand could be as high as 5 bracelets?

	Dual price of bracelet demand constraint (from the sensitivity report)	Increase in profit
A	0	0
B	0	0
C	4	4
D	0	0
E	0	0