Allocating resources

Nice work, time to solve the next problem you were introduced to.

A manager allocates 120 tasks to a senior (S), a junior (J) and an intern (I) software engineer and wants to minimize costs.

The intern requires training that costs $500 prior to working on the tasks. The cost to resolve each task is c = [30, 40, 5] respectively.

$x$ holds the number of assigned tasks and $o$ the binary for whether the intern receives training. The total cost is

$TC = 30x_S+40x_J+(5x_I+500)o$

Use the BigM method to linearize this problem using the new variable $z$:

$z = (5x_I+500)o$

$-oM\leq z \leq oM$

$-(1-o)M \leq z- (5x_I+500)o \leq (1-o)M$

pulp, along with a model, parameters c, M, and names, and variables x, z, o have already been imported for you.

Exercise