UML CS
Algorithms 91.503 (section 201)
Spring, 2006
Homework #8
Assigned: Monday, 4/17
Due: Monday, 4/24 at start of lecture
This assignment covers material on Chapter 29, Linear Programming.
1. (100 points) Consider the following problem:
Given: Dr. Salz treats cases of the disease flipitis with a combination of the
compounds Salium and Thimaze. Salium costs $0.40 per pill and Thimaze costs
$0.30 per pill. Each compound contains the ingredient SMD plus an activator. The
typical dosage requires at least 10 mg of SMD per day. One pill of Salium contains
4 mg of SMD and one pill of Thimaze contains 2 mg of SMD. In excessive amounts
the activators can be harmful, so the doctor makes the total activator amount at
most 2 mg per day. Salium and Thimaze each contain 0.5 mg of the activator per
pill.
How many of each pill should Dr. Salz prescribe to minimize the cost of the
medication, provide enough SMD, and not exceed the upper limit on the activator?
a) Formulate a linear program to solve the problem. Provide:
i.
Objective function
ii.
Objective function sense:
maximize
or
minimize (circle one)
iii.
Constraints
iv.
Variables: for each variable, list its meaning and provide bounds
b) Put your formulation into standard form.
c) Convert your answer to (b) into slack form.
d) Form the dual of your answer to (c).
e) Circle
i.
ii.
iii.
iv.
TRUE or FALSE for each statement below & briefly justify your choice.
The feasible region is bounded.
TRUE
FALSE
The feasible region is empty.
TRUE
FALSE
The feasible region is convex.
TRUE
FALSE
The objective function’s optimal value is bounded. TRUE
FALSE
f) Solve your linear program graphically (see attached grid). What is the optimal
value of your objective function? What are the values of your variables for this
optimal value?
g) Solve your linear program using SIMPLEX. What is the optimal value of your
objective function? What are the values of your variables for this optimal value?
Show the linear program resulting from each iteration of SIMPLEX.
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UML CS
Algorithms 91.503 (section 201)
2 of 2
Spring, 2006