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 $1,600$ for

machines $1$;$1,400$ for machine $2$ ; and $1,500$ for machine $3.$ The processing times are as follows:

Each component contains a different amount of two basic raw materials. Raw material $1$ costs $$0\mathrm{.}20$ per ounce, and raw material $2$ costs $$0\mathrm{.}35$ per ounce. At present, $202,000$ ounces

of raw material $1$ and $85,000$ ounces of raw material $2$ are available.

a$.$ Assume that the company must make at least $1,400$ 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 $=29\mathrm{.}4$ A $+17\mathrm{.}2$ B $+17\mathrm{.}05$ C$.($Enter your responses rounded to two decimal places.$)$

Constraints $($enter your responses rounded to two decimal places$)$:

b$.$ A linear programming software shows the optimal solution as: $B=1,400$ and $C=0.$ What is the optimal value for $A?$

$A=,.($Enter your response rounded to the nearest whole number.$)$