Problem $4(15$ points$)$Problem $2(20$ points$)$Problem $2(20$ points$)$

Labor fluctuating needs in construction projects can be met through hiring and end

employment. Both activities incur cost. The goal is to minimize the total cost of acquiring

needed labor force.

A contractor estimates that the size of the workforce needed over the next $5$ weeks is $5,7,8,4,$

and $6$ workers. Excess labor kept on the force will cost $$300$ per worker per week, and new

hiring in any week will incur a fixed cost of $$400$ plus $$200$ per worker per week.

Find the optimal solution for this problem through dynamic programming. How many workers

require for each period and what is the minimum total cost?

Labor fluctuating needs in construction projects can be met through hiring and end

employment. Both activities incur cost. The goal is to minimize the total cost of acquiring

needed labor force.

A contractor estimates that the size of the workforce needed over the next $5$ weeks is $5,7,8,4,$

and $6$ workers. Excess labor kept on the force will cost $$300$ per worker per week, and new

hiring in any week will incur a fixed cost of $$400$ plus $$200$ per worker per week.

Find the optimal solution for this problem through dynamic programming. How many workers

require for each period and what is the minimum total cost?

Cookie$-$baking project: the recipe provides the complete statement of work, from

which the work breakdown structure can be developed. The resources available for

this project are two cooks and one oven with limited capacity; the raw materials are the

ingredients to be used in preparing the cookie dough. As listed in following table, the

activities take a total of $80$ minutes of resource time. Because some activities can run

parallel, the cooks should complete the project in less than $80$ minutes.

Following table displays some of the planning that will save time in the project. For

example, once the oven is turned on$,$ it heats itself, freeing the cooks to perform other

activities. After the dough is mixed, both batches of cookies can be shaped; the

shaping of the second batch does not have to wait until the first batch is complete. If

both cooks are available, they can divide the dough in half and each cook can shape

one batch in the same four$-$minute period. However, if the second cook is not available

at this time, the project is not delayed because shaping of the second batch need not

be completed until the first batch exits the oven.

Imagine the start time is $8$ am$,$ use CPM $($critical path method$)$ to plan for this task.