$(1)$ The number of less$-$than$-$or$-$equal$-$to type constraints $($i$.$e$.$ these constraints involve two or more variables and do not include the upper or lower bound conditions$)$ in the formulation is equal to:

$($a$)2$

$($b$)3$

$($c$)4$

$($d$)5$

$($e$)$ None of the above

$(2)$ The number of greater$-$than$-$or$-$equal$-$to type constraints $($i$.$e$.$ these constraints involve two or more variables and do not include the upper or lower bound conditions$)$ in the formulation is equal to:

$($a$)1$

$($b$)2$

$($c$)3$

$($d$)4$

$($e$)$ None of the above

$(3)$ The number of equal$-$to type constraints $($i$.$e$.$ these constraints involve two or more variables and do not include the upper or lower bound conditions$)$ in the formulation is equal to:

$($a$)0$

$($b$)1$

$($c$)2$

$($d$)3$

$($e$)$ None of the above

$(4)$ Formulate the constraint that links the consumption $($or usage$)$ of wood with its availability?

$($a$)34x_1+5x_2+3x_{3}2400000$

$($b$)34x_1+57x_2+46x_{3}2400000$

$($c$)5x_1+57x_2+3x_{3}370000,$

$($d$)3x_1+6x_2+46x_{3}150000,(e)$ None of the above

$(5)$ Formulate the constraint that links the usage of cutting department time with its availability?

$($a$)34x_1+5x_2+46x_{3}2400000,($b$)3x_1+57x_2+6x_{3}150000$

$($c$)5x_1+9x_2+8x_{3}370000,($d$)37x_1+6x_2+8x_{3}370000,($e$)$ None of the above

$(6)$ Formulate the constraint that links the usage of finishing department time with its availability?

$($a$)3x_1+6x_2+4x_{3}150000,$

$($b$)4x_1+9x_2+46x_{3}2400000$

f $($c$)5x_1+57x_2+3x_{3}370000,$

$($d$)37x_1+6x_2+4x_{3}150000$

$($e$)$ None of the above

$(7)$ Which of the following is a valid constraint?

$($a$)x_1+y_1=28000,$

$($b$)x_2+y_{2}24000,$

$($c$)x_3+y_{3}21000,$

$($d$)x_3+y_{3}35000$

$($e$)$ all of the above

$(8)$ The objective function is: Min. $18\mathrm{.}50x_1+34\mathrm{.}70x_2+16\mathrm{.}40x_3+13\mathrm{.}20y_1+27\mathrm{.}50y_2+12\mathrm{.}30y_3.$

This statement is:

$($a$)$ True

$($b$)$ False