PROBLEM 5 Consider a two-period production model where 1,000 kgs of a certain product are required...

 

Transcribed Image Text:

PROBLEM 5 Consider a two-period production model where 1,000 kgs of a certain product are required in the first period (current period) and 1,000 kgs are required in the second period (future period).. In this production system, the output quantity P in kgs recovered from your production process is a fraction of the input quantity Q in kgs that you launch into your production process. Assume that a fraction of the input quantity launched into the process are lost due to factors beyond your control. Denote the output quantity by P = UQ where U is a random variable uniformly distributed between 0 and 1. Unfortunately, production cost depends on the input quantity, and is incurred at $10 per kg of input quantity. Furthermore, if you fail to deliver 1,000 kgs in each period, you incur a penalty of $20 per kg short. Determine the optimal production quantity in the first period. (20 pts) PROBLEM 5 Consider a two-period production model where 1,000 kgs of a certain product are required in the first period (current period) and 1,000 kgs are required in the second period (future period).. In this production system, the output quantity P in kgs recovered from your production process is a fraction of the input quantity Q in kgs that you launch into your production process. Assume that a fraction of the input quantity launched into the process are lost due to factors beyond your control. Denote the output quantity by P = UQ where U is a random variable uniformly distributed between 0 and 1. Unfortunately, production cost depends on the input quantity, and is incurred at $10 per kg of input quantity. Furthermore, if you fail to deliver 1,000 kgs in each period, you incur a penalty of $20 per kg short. Determine the optimal production quantity in the first period. (20 pts)