Question 1
The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420.
a. Plot the constraints on the grid below
b. Identify the feasible region and its corner points. Show your work.
c. What is the optimal product mix for this problem?
Question 2
The property manager of a city government issues chairs, desks, and other office furniture to city buildings from a centralized distribution centre. Like most government agencies, it operates to minimize its costs of operations. In this distribution centre, there are two types of standard office chairs, Model A and Model B. Model A is considerably heavier than Model B, and costs $20 per chair to transport to any city building; each model B costs $14 to transport. The distribution centre has on hand 400 chairs—200 each of A and B.
The requirements for shipments to each of the city's buildings are as follows:
Building 1 needs at least 100 of A
Building 2 needs at least 150 of B.
Building 3 needs at least 100 chairs, but they can be of either type, mixed.
Building 4 needs 40 chairs, but at least as many B as A.
Write out the objective function and the constraints for this problem. (Hint: there are eight variables—chairs for building 1 cannot be used to satisfy the demands for another building).
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