Demand and Supply Analysis

Jenny’s company has two running plants at locations A and B, with production capacity
KA = 5500 units and KB = 4500 units. The distance between locations A and B are 1000
kms. There are three markets, each having demand D = 4000 units. Two of them are at
locations A and B, respectively, and the third one is at location C, the mid-point between
A and B. Suppose the company produces each product at unit cost c = $25 and sells the
product at price p = $50 at each location. The transportation cost to ship a product from
a plant to a distant market is $0.02 per unit per km. Suppose there is no shortage cost.ABC
1) What is the company’s optimal profit under the current plant and market configuration? (5’)
2) Bobby is considering opening a new plant at location C. The new plant will have capacity KC = 3000 and there is a fixed cost $60,000 of opening it. Assume the production cost at location C is the same as other plants,c=$25per unit.Please help Bobby decide whether it is profitable to open this new plant.(5’)

3) Again consider opening a new plant at location C. Suppose the fixed cost of opening
a plant with capacity K is a ·K, where a is a cost parameter, and the production cost
at this plant is the same as other plants, c = $25 per unit. In this case, in addition
to deciding whether to open the plant, Bobby should also decide its capacity. Please

determine the range of a under which Bobby will open a new plant at location C. (5’)


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