hi! :) i need help on finding the constraints for this problem:

Question

An automotive company produces cars and trucks. Each vehicle must go through an assembly and painting process. If the painting part only paints the truck, 40 trucks can be painted in one day; if you only paint the car, 60 cars can be painted in one day. If the assembly part only assembles a car, 50 cars can be assembled in one day; if only assembling trucks, 50 trucks can be assembled in one day. Each truck produced will provide a profit of $ 300 and each car will give a profit of $ 200.

a. Formulate a linear programming model for the problem above.

b. Determine how many cars and trucks must be produced every day, using a graphical approach.

c. Complete the above problem using the simplex method

Answer 1

There are no constraints given, that's the problem.

It should say the factory has D_p days available for paining and D_a days available for assembly.

THe objective profit function is Profit(T,C) = 300*t + 200*c where t and c are the number of trucks and cars produced.

The time constraint for paining is T/40 + C/60 <= D_p

The time constraint for assembly is T/50 + C/50 <= D_a

(T+C)/50 <= D_a

T+C <= D_a*50

C <= D_a*50 - T

You can now solve this system by substitution, once you get these threshold constraints.

BTW, a good website for graphing is www.desmos.com