TV Manufactoring Problem Unconstraint
Variables
number of 19 in sets
number of 21-in sets
cost of manufacturing 19 in sets
cost of manufacturing 21 in sets
total cost
selling price of 19 in sets
selling price of 21 in sets
revenue
profit
Assumptions
Objective
Maximize P
We find all points with and
Maximum Profit
sensitivity of and to the elasticity of the 19 in sets and 21 inch sets
Our computations suggest that we should expect a 1.14% decrease in manufacturing of 19 in monitors for every 1% increase in the elasticity coefficient for 19 in monitors.
Our computations suggest that we should expect a 2.7% decrease in manufacturing of 21 in monitors for every 1% increase in the elasticity coefficient for 21 in monitors.
Computing the sensitivity of the maximum profit with respect to the elasticity of the 19 inch monitors
Sensitivity of the maximum profit using the chain rule (Alternate method)
Maximize subject to the constraint x = 5000.
The above point is outside of the feasible region and should not be used.
The above point is outside of the feasible region and should not be used.
The above point is a candidate for max
Maximize subject to the constraint x = 0
The above point is outside of the feasible point
Maximize P subject to the constraint y = 0.
The solution to the unconstraint problem is outside of the feasible region
Test Points
(5000,0)
(5000, 5000)
(50,000/13, 80,000/13)
(2000, 8000)
(0, 8000)
(0,0)
The result below suggests that if increases by 10%, decreases by 7.7%
The rsult below suggests that if increases by 10%, the maximum profit decreases by 2.8%
Sensitivity of the profit with respect to the condition
Suppose now that we have the constraint x<= 3000
Shadow price is to increase the c by one
to increase 19-inch by 1, you should'nt pay more than 22 dollars, to increase total production by one , you shouldn't pay more than $13.