an entrepreneur is setting up a storage facility which will provide storage both at peak times and off peak times.The entrepreneur need to decide how much money storage Q1 t to supply at peak times, and how much storage Q2 to supply off peak it also needs to decide how to set up capacity K, where capacity is such that both K is equal or plus Q1 and K is equal or plus Q2 The peak period demand fan storage is given by PI=7200 -Q1 and the off peak is give by P2=5400 -Q2 where P1 and P2 are the prices for units of storage at peak times and off peak respectively. the variable cost is 200 per unit of storage supplied and capacity costs are 100 per unit. Hence profits fpr the entrepreneurs are given by: (7200-Q1) Q1+ (5400-Q2) Q2 - 200 (Q1+Q2)-100 K where Q1 is less or equal K and Q2 is less or equal K a) write down the Kuhn-Tucken conditions for this proble. b) Find the optimal outputs and c
an entrepreneur is setting up a storage facility which will provide storage both
at peak times and off peak times.The entrepreneur need to decide how much money storage Q1 t to supply at peak times, and how much storage Q2 to supply off peak
it also needs to decide how to set up capacity K, where capacity is such that both K is equal or plus Q1 and K is equal or plus Q2
The peak period
the variable cost is 200 per unit of storage supplied and capacity costs are 100 per unit. Hence profits fpr the entrepreneurs are given by:
(7200-Q1) Q1+ (5400-Q2) Q2 - 200 (Q1+Q2)-100 K where Q1 is less or equal K and Q2 is less or equal K
a) write down the Kuhn-Tucken conditions for this proble.
b) Find the optimal outputs and capacity for this problem
c) now suppose there is a substancial increqse in capacity costs, which rise to 2000 per unit
find optimal capacity and peak and off peak storage
Step by step
Solved in 2 steps
