relevant costs Fisher manufacturingFisher Manufacturing Co$.$ produces and sells its product A$/100$ to well$-$known cosmetics companies for $$940$ per tonne. The marketing manager is considering the possibility of refining AA$100$ further into finer perfumes before selling them to the cosmetics companies. Product AA$101$ is expected to command a price of $$1,500$ per tonne, and AA$102$ a price of $$1,700$ per tonne. The maximum expected demand is $400$ tonnes for AA$101$ and $100$ tones for AA$102.$

The annual plant capacity of $2,400$ hours is fully utilized at present to manufacture $600$ tonnes of AA$100.$ The marketing manager proposed that Fisher sell $300$ tonnes of AA$100,100$ tonnes of AA$101,$ and $75$ tonnes of AA $102$ in the next year. It requires four hours of capacity to make one tonne of A$/100.$ two hours to refine AA$100$ further into AA$101,$ and four hours to refine AA$100$ into AA$102$ instead. The plant accountant has prepared the following cost sheet for the three products:

AA$100$

COSTS PER TONNE

A$101$

AA$102$

Direct materials:

Chemicals and fragrance

AA$100$

Direct labor

Manufacturing support: Variable

Fixed

Total manufacturing costs

Selling support:

Variable

Fixed

$$560$

$0$

$60$

$ $400$

$800$

$30$

$ $470$

$800$

$60$

$60$

$120$

$$800$

$30$

$60$

$$1,320$

$60$

$120$

$$1\mathrm{.}510$

$20$

$10$

$30$

$10$

$30$

$10$

$830$

$$1\mathrm{.}360$

$$1\mathrm{.}550$

$300$ tonnes

$600$ tonnes

$100$ tonnes

$400$ tonnes

$75$ tonnes

$100$ tonnes

Proposed sales level

Maximum demand

Required $-$

$($a$)$

Determine the production levels for the three products under the present constraint on plant capacity that will maximize operating income.

$($b$)$

Suppose a customer is very interested in the new product AAlOl. It has offered to sign a long$-$term contract for $400$ tonnes of AA$101.$ It is also willing to pay a higher price if the entire plant capacity is dedicated to the production of AA$101.$

What is the minimum price for AA$101$ at which it becomes worthwhile for Fisher to dedicate its entire capacity to the production of AA$101?$

$($c$)$

Suppose, instead, that the capacity can be increased temporarily by $600$ hours if the plant is operated overtime. Overtime premium payments to workers and supervisors will increase direct labor and variable manufacturing support costs by $50\%$ for all products. All other costs will remain unchanged. Is it worthwhile operating the plant overtime? If the plant is operated overtime for $600$ hours, what are the optimal production levels for the three products? Show details to