A small fabrication firm makes three basic types of components for use by other companies. Each component is processed on three machines. Total capacities$($in hours$)$ are for machines$1$; for machine$2$; and for machine $3.$ The processing times are as$$ follows:

Processing Time$($hr$)$

Component

Machine $1$

Machine $2$

Machine $3$

A

B

C

Each component contains a different amount of two basic raw materials. Raw material $1$ costs $$$ per$$ ounce, and raw material $2$ costs $$$ per ounce. At$$ present, ounces of raw material $1$ and ounces of raw material $2$ are available.

Requirements$($oz$/$unit$)$

Component

Raw Material $1$

Raw Material $2$

Selling Price$($$$/$unit$)$

A

B

C

Part $2$

a$.$ Assume that the company must make at least units of component$$ B$,$ that labor costs are$$ negligible, and that the objective is to maximize profits. Specify the objective function and constraints for the problem.

Objective$$ function: Maximize Z$=$

$$

enter your response hereA $+$

$$

enter your response hereB $+$

$$

enter your response hereC. $($Enter your responses rounded to two decimal$$ places.$)$