Stoneware Pottery Company wants to determine how many bowls and mugs should be p

Question

Stoneware Pottery Company wants to determine how many bowls and mugs should be produced per day in order to maximize profit given the labor and material constraints. The unit profit value for Bowls is $40 per unit, for mugs the unit profit value is $50 per unit. There are 40 hours of labor and 120 pounds of clay available per day. Each bowl requires 1 hour of labor and 4 pounds of clay to produce, each mug requires 2 hours of labor and 3 pounds of clay to produce.

a) Formulate a linear programming model for this problem to determine how many bowls and how many mugs should be produced in order to maximize the total profit.

b) Solve this problem by using the graphing method OR by using Excel Solver.

c) What is the optimal solution?

d) Which constraints are binding?

Please Show ALL Work.

Explanation / Answer

Let the constraints be x and y be the no of units of bowls and mugs

1x+2y< or equal to 40

4x+3y< or equal to120

Maximize the objective function i.e. z=40x+50y

Let the eq be 1x+2y=40

x=0, y=20 & x=40, y=0

4x+3y=120

x=0, y=40,,, x=30, y=0

4x+3y=120

now z=40x+50y

(x,y) (0,20)   z=40*0+50*20=1000

          (40,0) z=40*40+50*0=1600

           (0,40) z=40*0+50*40=2000

           (30,0) z=40*30+50*0=1200

            (24,8) z=40*24+50*8=1360

The company should produce 40 units of nmugs to maximize the profits

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