Winoc Sells

[BMAD]

Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below:

Resource Product 1 Product 2 Product 3 Product 4

Raw Material 2 3 4 7

Hours of labor 3 4 5 6

Sales Price ($) 4 6 7 8

Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?

Edited May 17, 2013 by BMAD

[dark_magician_92]

oh, i am sorry, just realised i had a calculation mistake earlier - none of 1st type, 400 of 2nd, 150 of 3rd and 400 of 4th type.

[BMAD]

4x₁+6x₂+7x₃+8x₄=z

s.t.

2x₁+3x₂+4x₃+7x₄<=4600

3x₁+4x₂+5x₃+6x₄<=5000

x₁+x₂+x₃+x₄=950

x₄>=400

x_1,x_2,x_3,x_{4 are integers}

[dark_magician_92]

400 of 1st type, 150 of 2nd and 400 of 4th type

[BMAD]

400 of 1st type, 150 of 2nd and 400 of 4th type

I do not have this as optimal

[BMAD]

400 of 1st type, 150 of 2nd and 400 of 4th type

If you consider x3 and x1, for every x3 you increase at the expense of an x1 (trade out) the sales increases and you are still within the constraints meaning more optimal profit.

[bushindo]

Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below:

Resource Product 1 Product 2 Product 3 Product 4

Raw Material 2 3 4 7

Hours of labor 3 4 5 6

Sales Price ($) 4 6 7 8

Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?

Here's my try

200 of product 1, 0 of product 2, 350 of product 3, 400 of product 4

[BMAD]

Winoc sells four types of products. The resources needed to produce one unit of each and the sales prices is listed below:

Resource Product 1 Product 2 Product 3 Product 4

Raw Material 2 3 4 7

Hours of labor 3 4 5 6

Sales Price ($) 4 6 7 8

Currently, 4,600 units of raw material and 5,000 labor hours are available.To meet customer demands, exactly 950 total units must be produced. Customers also demand that at least 400 units of product 4 be produced. What is the solution that maximizes Winoc's sales revenue?

Here's my try

200 of product 1, 0 of product 2, 350 of product 3, 400 of product 4

your solution produces revenue of 6450.

a revenue of 6650.