Problem $1$:

A tech company manufactures $15,000$ circuit boards each quarter. Each board sells for $$70.$ The labor input is $2,500$ hours at $$25/$hour$.$ The cost of materials is $$50,000,$ and the overhead cost is $2$ times the labor cost. Calculate the multifactor productivity.

Problem $2$:

A financial services firm processes $300$ client portfolios daily. The fee per portfolio is $$100.$ The firm uses $250$ hours of labor each day, costing $$35/$hour$.$ Additional daily costs include $$1,200$ for materials and three times the daily labor cost for overhead. Calculate the multifactor productivity.

Problem $3$:

In $2022,$ a customer support center had a labor productivity rate of $80$ support tickets per hour. By $2023,$ the productivity improved to $95$ support tickets per hour. Calculate the percentage of productivity growth from $2022$ to $2023.$

Problem $4$:

An auto workshop services $200$ cars a month, charging an average of $$600$ per service. The labor input is $1,800$ hours per month at a rate of $$25$ per hour. The cost of parts $($materials$)$ is $$40,000$ per month, and the overhead is equal to $1\mathrm{.}5$ times the total labor cost. Determine multifactor productivity.

Problem $5$:

In the first quarter of $2023,$ a textile plant produced $100,000$ garments with labor productivity at $100$ garments per hour. In the first quarter of $2024,$ the plant increased its labor productivity to $120$ garments per hour while producing $120,000$ garments. What is the percentage of productivity growth?

Problem $6$:

A project manager observed that a team completed $300$ deliverables over $150$ hours in one month. In the following month, the team completed $350$ deliverables but worked $180$ hours. Determine whether the team's productivity increased, decreased, or remained unchanged from one month to the next. Provide your reasoning and calculations to support your conclusion.