# Qdm Job

Quantitative Decision Making Models

Assignment # a couple of

QUESTION ONE

Decision Variables

Let,

* X1 = range of full-time tellers

2. Y1 = number of or perhaps tellers starting at being unfaithful a. m. (leaving in 1 s. m. ) * Y2 = range of part-time tellers starting at 10 a. m. (leaving at 2 p. meters. ) 2. Y3 = numbers of or perhaps tellers starting at 11 a. meters. (leaving for 3 p. m. ) * Y4 = range of part-time tellers starting at noon ( leaving for 4 l. m. ) * Y5 = volume of part-time tellers starting in 1 g. m. (leaving at your five p. meters. )

Goal Function

2. MIN 90X1 + 28(Y1 + Y2 + Y3 + Y4 + Y5)

Contraints

2. X1 + Y1 в‰Ґ 10 (9am-10am)

* 0. 5X1 + Y1 + Y2 в‰Ґ 12 (10am вЂ“ 11am)

* 0. 5X1 & Y1 & Y2 & Y3 в‰Ґ14 (11am вЂ“ noon) 2. X1 + Y1 + Y2 +Y3 + Y4 в‰Ґ 16 (noon вЂ“ 1pm)

* X1 & Y1 & Y2 & Y3 + Y4 + Y5 в‰Ґ 18 (1pm - 2pm)

* X1 + Y3 + Y4 + Y5 в‰Ґ 18 (2pm вЂ“ 3pm)

* X1 + Y4 + Y5 в‰Ґ 15 (3pm вЂ“ 4pm)

* X1 & Y5 в‰Ґ 10 (4pm вЂ“ 5pm)

* Back button < doze

* X1, Y1, Y2, Y3, Y4, Y5 в‰Ґ 0

Or perhaps workers cannot work more than 50% with the total hours required every day. Therefore , 4(Y1+Y2+Y3+Y4+Y5) в‰¤ zero. 50(10+12+14+16+18+17+15+10)

Maximum Solution

* X1 = 12

* Y1 = 0

* Y2 = several

* Y3 = 2

* Y4 = a few

* Y5 = zero

Optimal Benefit

bucks 1, 292 is the maximum value to minimize the total expense of employees operating.

QUESTION TWO

A)

Decision Variables

Permit,

* O1 = percentage of Oak units assigned to cabinetmaker you * T-MOBILE = percentage of Oak cabinets assigned to cabinetmaker 2 * O3 sama dengan percentage of Oak cabinetry assigned to cabinetmaker several * C1 = percentage of Cherry wood cabinets designated to cabinetmaker 1 5. C2 = percentage of Cherry units assigned to cabinetmaker two * C3 = percentage of Cherry wood cabinets given to cabinetmaker 3

Target Function

* Min 1800O1 + 1764O2 + 1650O3 + 2160C1 + 2016C2 + 1925C3 Contraints

2. 50O1 & 60C1 в‰¤40

* 42O2 + 48C2в‰¤30

* 30)3 + 35C3в‰¤35

* O1 + UNITED KINGDOM + O3=1

* C1 + C2 + C3=1

* O1, O2, O3, C1, C2, C3в‰Ґ0

B)

| Cabinet Developer 1| Pantry Maker 2| Cabinet Maker 3| Oak| 0. 271| 0| 0. 729

Cherry| 0| 0. 625| 0. 375

Therefore , to finish both assignments is assigning 27. 1% of the oak cabinets to Cabinet Maker 1 and 72. 9% to Case Maker 2 . For the Cherry, 62. 5% needs to be assigned to Cabinet Maker 2 and 37. 5% to Pantry Maker a few. Total cost of completing the two projects sama dengan \$ 3672. 500

C) Cabinetmaker 1 has a slack of 26. 458 several hours and a dual value of zero. This increases the right hand side of constraint 1 will not change the value with the optimal option.

D) The dual value for limitation 2 can be 1 . seventy five. The current Right-Hand-Side is 31 and allowable increase is usually 11. 143. The upper limit on Right-Hand-Side range is 41. 143. This means for every extra hour of time for Cabinet Maker 2, the overall cost will decrease simply by \$1. 75/hour, to a maximum of 41. 143 hours.

E) If cabinetmaker 2 reduces his cost to \$38 per hour, the modern objective function coefficients pertaining to O2 and C2 will be: 42(38) = 1596 and 48(38) = 1824. The perfect solution will not change however the total price decreases to \$3552. 40.

QUESTION THREE

Decision Variables

Let,

2. S =t the amount used stocks

2. B sama dengan the amount used bonds

2. M = the amount invested in mutual cash

* C = the quantity invested in Cash

* Ur = how much Risk

5. AR= total annual return

Target Functions

2. R sama dengan 0. 8S + zero. 2B +0. 3M & 0. 0C

* KVADRATMETER = 0. 1S + 0. 03B + 0. 04M & 0. 01C

Constraints

2. 10 в‰¤ C в‰¤ 30

5. M в‰Ґ B

2. S в‰¤ 75

5. S, M, M, C в‰Ґ 0

A) 3rd there’s r = zero. 8S & 0. 2B + zero. 3M & 0C

R = zero. 8(0. 409) + 0. 2(0. 145) + zero. 3(0. 145) + 0(0. 3)

Ur = zero. 3997

Hence the optimal share for this scenario is as comes after; S sama dengan 40. 9%, B sama dengan 14. five per cent, M sama dengan 14. five per cent, C sama dengan 30% that may create the perfect amount of risk, 0. 3997,...