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Radico manufactures two types of radios The only scare resource that is needed t

ID: 452782 • Letter: R

Question

Radico manufactures two types of radios The only scare resource that is needed to produce radio is labor. At present the company has two laborers Laborer 1 is willing to work up to 38 hours per week Laborer 2 will work up to 34 hours per week. Letting r, be the number of type i radios produced each week, Radioco should solve the following LP to maximize the profit: max z = 12x_1 + 8x_2 3x_1 + 2x_2 lessthanorequalto 38 Laborer 1 constraint 4x_1 + x_2 lessthanorequalto 34 Laborer 2 Constraint x_1,x_2 Greaterthanorequalto 0, where Si 2 is contribution to profit from per type 1 radio and $8 is contribution to profit from per type 2 radio. The optimal solution for this problem is X_1 = 6 x_2 = 10. (a) Find optimal z-value. (b) Find the slack variables and binding constraints. (c) Define the shadow price of the second constraint. Find the shadow price of constraint 1 (Laborer 1 constraint) (d) If the Laborer 1 were willing to work 42 hours per week, find the optimal value by using informal ion from part (c).(You only need information from part (c). do not need to solve).

Explanation / Answer

a) Optimal Z Value

= 12x1+8x2

= 12*6+8*10

= 152

b) If a constraint is binding, then the corresponding slack or surplus value will equal zero.