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A PRODUCTION AND INVENTORY APPLICATION 331
a. Develop a network representation of the problem.
b. Formulate the problem as a linear programme, with the optimal solution providing
the hours each consultant should be scheduled for each client in order to
maximize the consulting firm’s billings. What is the schedule and what is the total
billing?
c. New information shows that Avery doesn’t have the experience to be scheduled for
client B. If this consulting assignment is not permitted, what impact does it have on total
billings? What is the revised schedule?
7 Klein Chemicals, Inc., produces a special oil-based material that is currently in short
supply. Four of Klein’s customers have already placed orders that together exceed the
combined capacity of Klein’s two plants. Klein’s management faces the problem of
deciding how many units it should supply to each customer. Because the four customers
are in different industries, different prices can be charged based on the various industry
pricing structures. However, slightly different production costs at the two plants and
varying transportation costs between the plants and customers make a ‘sell to the highest
bidder’ strategy questionable. After considering price, production costs and transportation
costs, Klein has established the following profit per unit for each plant–customer
alternative.
Customer
Plant D 1 D 2 D 3 D 4
Clifton Springs E32 E34 E32 E40
Danville E34 E30 E28 E38
The plant capacities and customer orders are as follows:
Plant Capacity (units) Customer Orders (units)
Clifton Springs 5 000 D 1 2 000
D 2 5 000
Danville 3 000 D 3 3 000
D 4 2 000
How many units should each plant produce for each customer to maximize profits? Which
customer demands will not be met?
8 The Bahrain Manufacturing Company has orders for three similar products:
Product Orders (units)
A 2 000
B 500
C 1 200
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