Question

A manufacturer produces two products, P and Q, which when sold earn contributions of  £600 and  £400 per unit respectively.  The manufacturer of each product requires time on a lathe and a polishing machine. Each unit of P requires 2 hours on the lathe and 1 hour on the polishing machine, while Q requires 1 hour on each machine.  Each day, 10 hours are available on the lathe and 7 hours on the polishing machine.  Determine the number of units of P and Q that should be produced per day to maximize contribution.

1. set up the problem in mathematical form.
2. Solve the problem, using either the graphical or computer method.
3. Show the graph of the feasible region, or turn in the computer output.
4. Give the values of the decision variables and the objective function for the solution.

Answer 1

Give us a chance to expect that 'x' units of P and 'y' units of Q ought to be created.

Commitment is given by the capacity:

f(x,y) = 600*x + 400*y

Constraints are given by:

2*x + y <= 10

x + y <= 7

We need to maximize the given capacity f(x,y) subject to the above constraints.

max{600 x + 400 y|x + y<=7 && 2 x + y<=10 && x<=10 && x>=0 && y>=0} = 3400 at (x, y) = (3, 4)

Thus, for maximum contribution:

(x,y) = (3,4)