Linear Programming

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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

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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.