Section 3, Problem 8

Data from difficulty 7.

Formulate LPM to determine the number of basketballs and footballs to generate in order to increase profit. X1 -- # of basketballs

X2 -- # of footballs

Maximize Z . = 12x1 + 16x2

Subject to:

3x1 + 2x2 ≤ five-hundred

4x1 & 5x2 ≤ 800

X1, x2 ≥ 0

Convert this model to standard kind.

Maximize Unces = 12x1 + 16x2 + 0s1 +0s2

3x1 + 2x2 & s1 sama dengan 500

4x1 +5x2 + x2 sama dengan 800

X1, x2, s1, s2 ≥ 0

a). Identify how much unused methods (slack) at each of the graphic points. 3x1 + 2x2= 5004x1 & 5x2 = 800

X1 = 0, x2 = 250 X1 = 0, x2 = 160

X2 = 0, x1 = 500/3X2 sama dengan 0, x1 = 2 hundred

Maximize Z = 12x1 + 16x2

At level A (0, 0)Z sama dengan 0

At point W (500/3, 0) Z sama dengan 12(500/3) + 16(0) Z . = 2150

At level D (0, 160) Z . = 12(0) + 16(160)Z = 2560

At stage C (900/7, 400/7) Unces = 12(900/7) +16(400/7) Unces = 2457

Point M (0, 160) is an optimal remedy. X1 sama dengan 0, x2 = one hundred sixty, Z = 2560 Abandoned resources:

For point G (0, 160)

3x1 + 2x2 + s1 sama dengan 5004x1 +5x2 + s2 = 800

3(0) + 2(160) & s1 = 5004(0) & 5(160) +s2 = 800

S1 = 500 -320s2 = 800 - 800

S1 sama dengan 180s2 = 0

For point C (900/7, 400/7)

3(900/7) +2(400/7) + s1 = 5004(900/7) + 5(400/7) + s2 = 800 2700/7 +800/7 + s1 = 5003600/7 +2000/7 + s2 sama dengan 800

S1 = 3500/7 -500s2 sama dengan 800 – 5600/7

S1 = 0s2 = 0

At stage B (500/3, 0)

3(500/3) + 2(0) + s1 = 5004(500/3) +5(0) +s2 = 800

500 & s1 = 5002000/3 & s2 sama dengan 800

S1 = 0s2 = 400/3

At level A (0, 0)

3(0) +2(0) & s1 sama dengan 5004(0) +5(0) +s2 = 800

S1 = 500s2 = 800

b). What would be effect on the perfect solution if the profit for any basketball improved from $12 to $13? Z sama dengan 12x1 + 16x2 becomes Z sama dengan 13x1 & 16x2

By point M (0, 160) Z sama dengan 2560

In point N (500/3, 0)Z = 2166. 67

By point C (900/7, 400/7) Z = 2585. 71

Point C would become an optimal solution in the event that profit pertaining to basketballs transformed from $12 to $13.

What would be the result if the profit for a basketball changed by $16 to $15?...