Tom Ltd$.$ has two constraints: labour, limited to $16,000$ hours, and materials, limited to

$15,000$kg$.$ The firm manufactures and sells two products, X and Y$.$ To make X$,$ the firm

uses three kgs of material and four hours of labour, whereas to make Y$,$ the firm uses

five kgs of material and four hours of labour. The selling price per unit is $94$ and $120$

for X and Y respectively. The cost of materials is normally $8$ per kg$,$ and the labour

rate is $10$ per hour.

$11.$Tom$$s Ltd$.$ objective function is:

$($a$)30$X $+40$Y

$($b$)94$X $+120$Y

$($c$)64$X $+80$Y

$($d$)24$X $+40$Y