COMPANY PHONESKAREN DANIELA CUERVO CELY

FABIAN ESTEBAN GONZALEZ GARAVITO

TELBOY(TELEPHONY BOYACÁ)

TELBOY producing for high-end mobile Smartphone, including the display and batteries which are assembled to the phone body. 3 floors, the first is where the glass and ITO for mobile occurs, where the second and third stack which is assembled is manufactured.

Product 1: Display glass and ITO.Product 2: Battery for Smartphone.

The product 1 of the required capacity in the plants 1 and 3; 2 needs the product of the work of levels 2 and 3.

Determine what production rates should have two products in order to maximize total profits, subject to the restrictions imposed by limited production capacity available in the 3 levels.

Facts:● Number of production hours

available per week in each plant to manufacture the products.

● Hours of manufacture are used to produce each batch (50 units) of each new article in each of the plants.

● Earnings per batch of each new product.

Formulation as a linear programming problem

X1 = number 1 batch of product is manufactured by week.X2 = Product Lot Number 2 being manufactured per week.Z = total weekly earnings generated by these products.

PLANTBatch production

time, hoursproduct

1 2

Available production time per week, hours.

123

4 0 0 5 4 3

91420

Earnings per Lot $6000 $4000

Maximize Z= 6X1 + 4X2

4X1<= 9

5X2<=14

4X1 + 3X2 <= 20

X1>= 0, X2>=0

2, 25

2,8 4x1 <=9

5x2 <= 14

4x1 + 3x2 <=20

Z = 6X1 + 4X2Z = 6(2)Z= 12

X1 = 2

Z = 4X212 = 4X212/4 = X2X1 = 3

When z=0 when Z=12

Max Z= 6X1 + 4X2

X1 = 2,25X2 = 2,8

Maximize Z = 6X1 + 4X2

Sujeta a

4X1 <= 9

5X2 <=14

4X1 + 3X2 <= 20

X1>= 0, X2>=0

Minimize W = 9Y1 + 14Y2 + 20Y3

Sujeta a

4Y1 + 4Y3 >= 6

5Y2 + 3Y3 >= 4

Y1, Y2, Y3 >= 0

SIMPLEX DUAL

If the value of the number of hours of production batches of the product number 1 which is manufactured by week 9-11 changed the gain is increased.