Question

a manufacturer experiences a strong seasonal demand pattern, driven by the winter holiday season. the company has a 6 - month production plan, where the monthly demands dt are provided in the table below. the unit cost, fixed setup cost, and monthly holding cost for each unit is provided in the table below. based on this information, what is the optimal production schedule for the 6 - month period using the wagner - whitten algorithm. (similar to problem 9)

t	1	2	3	4	5	6
ct	$1,000	$1,000	$1,000	$1,000	$1,000	$1,000
at	$15,000	$15,000	$15,000	$15,000	$15,000	$15,000
ht	$1	$1	$1	$1	$1	$10

build lot for lot, so build period 1 in period 1, period 2 in period 2, period 3 in period 3, etc.
build periods 1, 2, 3, & 4 in period 1, build periods 5 & 6 in period 5.
build periods 1 & 2 in period 1, build period 3 in period 3, build period 4 in period 4, build periods 5 & 6 in period 5

question 18
10 pts
the economic lifetime of a particular model of phone is only 6 to 12 months. for a new model of phone that is about to be released, a company needs to negotiate a contract with a screen provider. the company is forecasting the demand of the phone to be a normal distribution with a mean of 3.1 million units with a standard deviation of 250,000 units. the net profit from each units sale is $525. each screen has a cost of $175 and are not expected to be available for salvage. use the news vendor model to determine the purchase quantities of screens where the cost of lost sales and cost of excess materials are balanced. (similar to problem 11)
3,179,660
389,660
10,797
3,268,622

Explanation:

Step1: Identify relevant costs for news - vendor model

The cost of under - stocking $C_u$ is the net profit per unit, $C_u = 525$. The cost of over - stocking $C_o$ is the cost per screen, $C_o=175$.

Step2: Calculate the critical ratio

The critical ratio $CR=\frac{C_u}{C_u + C_o}=\frac{525}{525 + 175}=\frac{525}{700}=0.75$.

Step3: Use the standard normal distribution

We know that the demand $D$ follows a normal distribution with mean $\mu = 3100000$ and standard deviation $\sigma=250000$. We need to find the $z$ - value corresponding to the critical ratio $CR = 0.75$. Looking up in the standard normal table, the $z$ - value $z\approx0.6745$.

Step4: Calculate the optimal order quantity

The formula for the optimal order quantity $Q$ in the news - vendor model for a normal distribution is $Q=\mu+z\sigma$. Substituting the values, we get $Q = 3100000+0.6745\times250000=3100000 + 168625=3268625\approx3268622$ (rounding to the nearest whole number).

Answer:

3,268,622