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King Supply makes four different types of plumbing fixtures: $W,x,Y$ and $Z.$ The contribution margins for these products are: $$70$ for Product $W,$$$60$ for Product $x,$$$90$ for Product $Y$ and $$100$ for Product Z$.$ Fixed overhead is estimated at $$5,500$ per week. The manufacture of each fixture requires four machines, Machines #$1,2,3$ and $4.$ Each of the machines is available for $40$ hours a week and there is no setup time required when shifting from the production of one product to any other. The processing requirements to make one unit of each product are shown in the table. Weekly product demand for the next planning period has been forecasted as follows: $70Ws,60xs,50$ Ys and $30Zs.($CLO$4)$

$\backslash$table$[[,$Processing Time $($min$/$fixture$),],[$Machine$,$W$,x,Y,Z$