$1,500$ for machine $2$ ; and $1,600$ for machine $3.$ The processing times are as follows:

Processing Time $($hr$)$

$\backslash$table$[[$Component$,$Machine $1,$Machine $2,$Machine $3],[$A$,0\mathrm{.}25,0\mathrm{.}10,0\mathrm{.}05],[$B$,0\mathrm{.}20,0\mathrm{.}15,0\mathrm{.}10],[$C$,0\mathrm{.}10,0\mathrm{.}05,0\mathrm{.}15]]$

$1$ and $110,000$ ounces of raw material $2$ are available.

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

$\backslash$table$[[$Requirements $($oz$/$unit$)],[$Component$,$Raw Materlal $1,$Raw Material $2,$Selling Price $($$$/$unit$)],[$A$,32,12,40\mathrm{.}00],[$B$,26,16,28\mathrm{.}00],[$C$,19,9,24\mathrm{.}00]]$

constraints for the problem.

Objective function: Maximize $Z=29\mathrm{.}40A+17\mathrm{.}20B+17\mathrm{.}05C.($Enter your responses rounded to two decimal places.$)$

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

Machine $1(C_1)$ :

Machine $2(C_2)$ :

Machine $3(C_3)$ :

Material $1(C_4)$ :

$\backslash$table$[[0\mathrm{.}25A+0\mathrm{.}20B+0\mathrm{.}10C,1600],[0\mathrm{.}10A+0\mathrm{.}15B+0\mathrm{.}05C,1500],[0\mathrm{.}05A+0\mathrm{.}10B+0\mathrm{.}15C,1600]]$

Material $2(C_5)$ :

$32A+26B+19C204000$

Minimum for product $(C_6)$ :

$12A+16B+9C110000$

Nonnegativity:

$B1,200$

$A0,B0,C0$

b$.$ A linear programming software shows the optimal solution as: $B=1,200$ and $C=0.$ What is the optimal value for $A?$