Question

Note: Treat each product as a separate problem and follow the solution procedure of the similar problem I did in the class. Contact me on Monday should you need help. 1. You start your own company, AM-Logistics. Your company got a contract from military to supply two products, AM1 and AM2. Your normal production cost is $40 per unit to produce each of the products and sell them to your customer (military) for $70 per unit. The monthly demand for the two products and their probabilities are stated below. Demand (units) AM1 (probability) AM2 (probability) 100 0.2 0.2 200 0.2 300 0.5 0.3 400 0.2 0.3 You are required to determine the production capacity of each product. If the demand is more than your normal capacity in a month, you need to work overtime and purchase your supplies and raw material for your products at a premium and your production costs goes up to $80 per unit rather than just $40. Note that you must meet your customer's demand every month. If military demand is less than your capacity, you can always sell either product to another customer for $35 per unit. Your objective is to maximize profits from making and selling each product. a. Determine the optimal capacity for PM1 and PM2. b. Determine the cost of perfect information for each product.

Answer 1

a)

The optimal capacity denotes the ability of an entity in producing more output using fewer costs. It can also say this concept as the optimum utilization of the available resources held by an entity.

Existing case

Currently, AM logistics sell goods for $70 per unit and its production cost is $40. Now with the changes in the demand, the production costs rose from $40 to $80 per unit and selling price of $35 in case of less demand.

Demand	PM1	PM2
100	20	20
200	40	60
300	150	90
400	40	80

Production costs per unit= $40 per unit if demand is higher than $80

Seling price= $70 per unit

Particulars	PM1				PM2
Demand	20	40	150	40	20	60	90	80
Production costs	$800	$1600	$12000	$1600	$800	$4800	$7200	$6400
Selling price	$1400	$2800	$5250	$2800	$1400	$4200	$3150	$5600
Optimum capacity	OPtimal capacity is 150 units where the cost of production is $80.				Optimal capacity is 90units where the cost of production is $80.

b)

An entity will get to know about the potential of the production using perfect information value which is a forecasting tool in taking decisions for an entity.

Demand	Production costs(AM1)	Probability	Px(price information)
20	$800	0.2	$160
40	$1600	0.2	$320
150	$12000	0.5	$6000
40	$1600	0.1	$160
EV(perfect information)			$6640
Expected value without information			$1608
Perfect valuation(EV with information/without information)			$4.106

Demand	Production costs(AM1)	Probability	Px(price information)
20	$800	0.2	$160
60	$4800	0.3	$1440
90	$7200	0.3	$2160
80	$6400	0.2	$1280
EV(perfect information)			$5040
Expected value without information			$4818
Perfect valuation(EV with information/without information)			$1.04