Question

Hello Dolly, Inc. crafts three styles of dolls: Lexi, Maysy, and Dizzy. Each doll requires sewing time, painting time, and supplies. Sewing machines are available for only 206 hours, only 2760 hours are available for painting, and 666.5 lbs. of supplies are available. Each Lexi doll requires 0.6 hours of sewing, 9 hours of painting, and 1.3 lbs. of supplies. Each Maysy doll requires 0.8 hours of sewing, 6 hours of painting, and uses 2 pounds of supplies. Each Dizzy doll requires 0.4 hours of sewing, 8 hours of painting, and 2.3 pounds of supplies. If the company earns a profit of $105 per Lexi doll, $125 per Maysy doll, and $130 per Dizzy doll, how many of each doll should the company produce to maximize profit? How much profit will result? (Use x for the number of Lexi dolls, y for the number of Maysy dolls, and z for the number of Dizzy dolls.) Maximize P = Preview subject to Preview <206 Preview < 2760 Preview < 666.5 Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed, round dolls to the nearest whole and profit to 2 decimal places. Number of Lexi dolls to maximize profit is Number of Maysy dolls to maximize profit is Number of Dizzy dolls to maximize profit is Maximum profit is $ Submit License Question 6. Points possible: 12 This is attempt 1 of 4. Message instructor about this question

Answer 1

Let the company should produce x​​​​​ number of Lexi dolls , y  number of Maysy dolls and z number of Dizzy dolls to maximize the profit.

Maximize P = 105x + 125y + 130 z

Subject to 0.6x + 0.8y + 0.4z <= 206

9x + 6y + 8z <= 2760

1.3x + 2y + 2.3z <= 666.5

x,y,z >=0

Initial values: X1 X2 X3 S1 S2 S3 BFS Z -105 -125-130 0 0 0 0 S1 3/5 4/5 2/5 1 0 0 206 S2 9 6 8 0 1 0 2760 S3 13/10 2 23/10 0 0 1 1333/2| The start table: X1 X2 X3 S1 S2 S3 BFS z -105 -125-130 0 0 0 0 51 3/5 4/5 2/5 1 0 0 206 S2 9 6 8 0 1 0 2760 S3 13/10 2 23/10 0 0 1 1333/2

Iteration: 1 X1 X2 X3 S1 S2 S3 BFS z -725/23-275/23 0 0 0 1300/23150687/4 51 43/115 52/115 0 1 0 -4/23 2072/23 S2 103/23 -22/23 0 0 1 -80/23 10160/23 X3 13/23 20/23 1 0 0 10/23 6665/23 Iteration: 2 X1 X2 X3 S1 S2 S3 BFS z 0 -1925/103 0 0 725/1033300/103570935/14 S10 274/515 0 1 -43/515 12/103 5480/103 X1 1 -22/103 0 0 23/103 -80/103 10160/103 X30 102/103 1 0 -13/103 90/103 24105/103 Iteration: 3 X1 X2 X3 S1 S2 S3 BFS z 0 0 0 9625/2741125/2744950/13742650 X2 0 1 0 515/274 -43/274 30/137 100 X1 1 0 0 55/137 26/137 -100/137 120 X3 0 0 1 -255/137 4/137 90/137 135 |

The optimal solution is: Z = 42650 X1 = 120 X2 = 100 x3 = 135 S1 = 0 S2 = 0 S3 = 0
Number of Lexi dolls to maximize the profit is 120.

Number of Maysy dolls to maximize the profit is 100.

Number of Dizzy dolls to maximize the profit is 135.