8.1 Merrill Sporting Goods (Revisited) Revisit Example 8.4, in which the criterion gives equal weight to each of the retail sites. But in practice, there will be different levels of traffic between the warehouse and the various sites. One way to incorporate this consideration is to estimate the number of trips between the warehouse and each retail site and then weight the distances by the trip volumes. Thus, the original data set has been augmented with volume data (vk), as listed in the table below.
|
Site (k)
|
xk
|
Yk
|
vk
|
|
1
|
9
|
29
|
12
|
|
2
|
5
|
50
|
15
|
|
3
|
26
|
68
|
20
|
|
4
|
39
|
79
|
12
|
|
5
|
41
|
54
|
8
|
|
6
|
38
|
59
|
16
|
|
7
|
63
|
6
|
18
|
|
8
|
52
|
58
|
20
|
|
9
|
81
|
76
|
12
|
|
10
|
95
|
93
|
24
|
Now we can use as a criterion the weighted sum of distances between the warehouse and the retail sites.
What location is optimal for the weighted version of the criterion?
How much of an improvement is achieved by the solution in (a) over the optimal location for the unweighted version (39.59, 58.43)?
8.6 Pricing with Dependent Demands Covington Motors is a car dealership that specializes in the sales of sport utility vehicles and station wagons. Due to its reputation for quality and service, Covington has a strong position in the regional market, but demand is somewhat sensitive to price. After examining the new models, Covington's marketing consultant has come up with the following demand curves.
The dealership's unit costs are $17,000 for SUVs and $14,000 for wagons. Each SUV requires 2 hours of prep labor, and each wagon requires 3 hours of prep labor. The current staff can supply 320 hours of labor.
Determine the profit-maximizing prices for SUVs and Wagons. (Round off any fractional demands.)
What demand levels will result from the prices in (a)?
What is the marginal value of dealer prep labor?
8.7 Pricing with Interdependent Demands Covington Motors sells sport utility vehicles and station wagons in a price-sensitive market. Its marketing consultant has rethought the simple demand curves first proposed (in the previous exercise) and now wants to recognize the interaction of the two markets. This gives rise to a revised pair of demand curves for SUVs and wagons, as shown below.
The dealership's unit costs are $17,000 and $14,000 per unit, respectively. Each SUV requires 2 hours of prep labor, and each Wagon requires 3 hours of prep labor. The current staff can supply 320 hours of labor. Covington Motors wants to maximize its profits from the SUVs and Wagons that it acquires for its stock.
Determine the profit-maximizing prices for SUVs and Wagons. (Ignore the fact that these prices may induce fractional demands.)
What sales levels will result from the prices in (a)?
What is the marginal value of dealer prep labor?
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