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.
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