Lineær Programmering

Hejsa,

Jeg sidder med en opageve i operationsanlyse der handler om at opstille et lineært problem, udfra informationerne i teksten.

Jeg kan ikke rigtige gennemskue hvordan den skal stilles op:

Den skal bare opstilles på almindelig standard form dvs.:

maximize: c₁x₁+c₂x₂+...+c_nx_n

subject to: a₁₁x₁+a₁₂x₂+....+a_1nx_n ≤ b₁

                    a₂₁x₁+a₂₂x₂+....+a_2nx_n ≤ b₂

                   osv.

Opgave:

A steel company must decide how to allocate next weeks time on a rolling mill, which is a machine that takes unfinished slabs of steel as input and can produce either of two semi-finished products: Bands and Coils. The mill's two product come off the rolling line at different rates: Bands: 200 tons/hr and Coils: 140 tons/hr.

They also produce different profits: Bands: $25/ton and Coils: $30/ton

Bases on a currently booked orders, the follow upper bounds are placed on the amount of each product to produce:

Bands: 6000 tons and Coils 4000 tons

Given that there are 40 hours of production availble this week, the problem is to decide how many tons of bands and how many tons of coils should be produced to yeld the greatest profit. Formulate this problem as linear programming problem.

Jeg tror umiddelbart min max funktion bliver: 25*200x₁ + 30*140x₂ = 5000x₁+4200x₂  

Jeg har dog svært ved at se hvordan begrænsninger skal stilles op.

Håber der er nogen som kan hjælpe.