# programing problem

Page 394

1) A particular linear programing problem is formulated as follows:

Min. Z= 2500x+3500y

Subject to:

5x + 6y > 250

4x + 3y > 150

x + 2y > 70

x, y > 0

Draw these constraints on graph paper (or excel) and determine the optimum solution.

a. Set up the problem in mathematical form

b. Solve the problem by the graphical method

Page 394-395

2) A manufacturer produces two products, P and Q, which when sold earn contributions of $600 and $400 per unit respectively. The manufacture 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.

a. Set up the problem in mathematical form

b. Solve the problem, using either graphical or computer method, show your work.