Case 3.1 (Auto Assembly)

(1)

GIVEN

Profit Labour Hours Doors Demand

1.0 Family Thrillseeker 3,600 6.0 - -2.0 Classy Cruiser 5,400 10.5 - 3,500 3.0 Total Availability - 48,000 20,000

-KEY DECISIONS

1.0 Let the Number of Family Thrillseeker be X

2.0 Let the Number of Classy Cruiser be Y

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 48000 6 11 48,000 3.0 Y ≤ 3500 - 1 3,500 4.0 X ≥ 0, Y ≥ 0 Z 3.0 - 1 3,500 1,875 2.0 6 11 48,000 3,500 1.0 4 2 20,000 3,800 2.0 6 11 48,000 2,400 1.0 4 2 20,000 5,000 4.0 - - -

-Therefore, to maximize total profit, 3800 Family Thrillseeker and 2400 Classy Cruiser should be assembled. This will generate total profit of $26640000.

CASE 3.1

Sub-Section (a) 26,640,000 Product 25,650,000 18,000,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(2)

GIVEN

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 48000 6 11 48,000 3.0 Y ≤ 4200 - 1 4,200 4.0 X ≥ 0, Y ≥ 0 Z 2.0 6 11 48,000 650 3.0 - 1 4,200 4,200 1.0 4 2 20,000 3,800 2.0 6 11 48,000 2,400 1.0 4 2 20,000 5,000 4.0 - - - - 18,000,000

Therefore, to maximize total profit, 3800 Family Thrillseeker and 2400 Classy Cruiser should be assembled and increase in demand of Classy Cruiser by 20% will not effect our decision

CASE 3.1

Sub-Section (b) Product 25,020,000 26,640,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(3)

GIVEN

Profit Labour Hours Doors Demand 1.0 Family Thrillseeker 3,600 6.0 - -2.0 Classy Cruiser 5,400 10.5 - 3,500 3.0 Total Availability - 60,000 20,000

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 60000 6 11 60,000 3.0 Y ≤ 3500 - 1 3,500 4.0 X ≥ 0, Y ≥ 0 Z 2.0 6 11 60,000 3,875 3.0 - 1 3,500 3,500 1.0 4 2 20,000 3,000 2.0 6 11 60,000 4,000 1.0 4 2 20,000 3,250 3.0 - 1 3,500 3,500 1.0 4 2 20,000 5,000 4.0 - - - - 18,000,000

(c) To maximize total profit, 3250 and 3500 should be assembled. This will generate total profit of $30600000; and (d) A total cost of $3960000 (30600000 - 26640000) can be the max viable cost of Overtime.

30,600,000

CASE 3.1

Sub-Section (c) & (d) Product 32,850,000 32,400,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(4)

GIVEN

Profit Labour Hours Doors Demand 1.0 Family Thrillseeker 3,600 6.0 - -2.0 Classy Cruiser 5,400 10.5 - 4,200 3.0 Total Availability - 60,000 20,000

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 60000 6 11 60,000 3.0 Y ≤ 4200 - 1 4,200 4.0 X ≥ 0, Y ≥ 0 Z 2.0 6 11 60,000 2,650 3.0 - 1 4,200 4,200 1.0 4 2 20,000 3,000 2.0 6 11 60,000 4,000 1.0 4 2 20,000 2,900 3.0 - 1 4,200 4,200 1.0 4 2 20,000 5,000 4.0 - - - -33,120,000 18,000,000

(e) To maximize total profit, 3000 Family Thrillseeker and 4000 Classy Cruiser should be assembled. This will generate total profit of $32400000; and (f) The incremental profit is $5760000 whereas incremental cost of Overtime and Advertising Campaign is $2,100,000. The idea, should therefore, be implemented

CASE 3.1

Sub-Section (e) & (f)

Product 32,220,000 32,400,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(5)

GIVEN

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 2800X + 5400Y 2,800 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 48000 6 11 48,000 3.0 Y ≤ 3500 - 1 3,500 4.0 X ≥ 0, Y ≥ 0 Z 2.0 6 11 48,000 1,875 3.0 - 1 3,500 3,500 1.0 4 2 20,000 3,800 2.0 6 11 48,000 2,400 1.0 4 2 20,000 5,000 4.0 - - - - 14,000,000 Therefore, to maximize total profit, 1875 Family Thrillseeker and 3500 Classy Cruiser should be assembled. This will generate total profit of $24150000.

CASE 3.1

Sub-Section (g) Product 24,150,000 23,600,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(6)

GIVEN

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 7.5X + 10.5Y ≤ 48000 8 11 48,000 3.0 Y ≤ 3500 - 1 3,500 4.0 X ≥ 0, Y ≥ 0 Z 3.0 - 1 3,500 1,500 2.0 8 11 48,000 3,500 1.0 4 2 20,000 4,222 2.0 8 11 48,000 1,556 1.0 4 2 20,000 5,000 4.0 - - - - 18,000,000

Therefore, to maximize total profit, 1500 Family Thrillseeker and 3500 Classy Cruiser should be assembled. This increased labour hour will generate total profit of $24300000.

CASE 3.1

Sub-Section (h) Product 24,300,000 23,600,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(7)

GIVEN

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 3600X + 5400Y 3,600 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 6X + 10.5Y ≤ 48000 6 11 48,000 3.0 Y ≤ 3500 - 1 3,500 4.0 X ≥ 0, Y ≥ 0 Z 3.0 - 1 3,500 1,875 2.0 6 11 48,000 3,500 1.0 4 2 20,000 3,800 2.0 6 11 48,000 2,400 1.0 4 2 20,000 5,000 4.0 - - - - 18,000,000 Therefore, to maximize total profit, 1875 Family Thrillseeker and 3500 Classy Cruiser should be assembled. This will generate total profit of $25650000, i.e. decrease in profit of

$990000.

CASE 3.1

Sub-Section (i) Product 25,650,000 26,640,000 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0

(8)

GIVEN

-KEY DECISIONS

OBJECTIVE FUNCTION 1.0 Maximize Z = 2800X + 5400Y 2,800 5,400 -CONSTRAINTS 1.0 4X + 2Y ≤ 20000 4 2 20,000 2.0 7.5X + 10.5Y ≤ 60000 8 11 60,000 3.0 Y ≤ 4200 - 1 4,200 4.0 X ≥ 0, Y ≥ 0 Z 2.0 8 11 60,000 2,120 3.0 - 1 4,200 4,200 1.0 4 2 20,000 3,333 2.0 8 11 60,000 3,333 1.0 4 2 20,000 5,000 4.0 - - - - 14,000,000 Therefore, to maximize total profit, 2120 Family Thrillseeker and 4200 Classy Cruiser should be assembled. This will generate total profit of $28616000.

CASE 3.1

Sub-Section (j) Product 28,616,000 27,333,333 2,000 4,000 6,000 8,000 10,000 12,000 - 2,000 4,000 6,000 8,000 10,000 12,000 1.0 2.0 3.0