$7\mathrm{.}3.$ Vendor Allocation with Price Breaks Universal Technologies, Inc. has identified two qualified vendors with the capability to supply some of its electronic components. For the coming year, Universal has estimated its volume requirements for these components and obtained price$-$break schedules from each vendor. $($These are summarized as "all$-$units" price discounts in the table below.$)$ Universal's engineers have also estimated each vendor's maximum capacity for producing these components, based on available information about equipment in use and labor policies in effect. Finally, because of its limited history with Vendor A$,$ Universal has adopted a policy that permits no more than $60\%$ of its total unit purchases on these components to come from Vendor A$.$

$\backslash$table$[[$Product$,$Requirement,Vendor A$,$Vendor B$],[\backslash$table$[[$Unit$],[$price$]],\backslash$table$[[$Volume$],[$required$]],\backslash$table$[[$Unit$],[$price$]],\backslash$table$[[$Volume$],[$required$]]],[1,500,$$$225,0-250,$$$224,0-300],[$$$220,250-500,$$$214,300-500],[2,1000,$$$124,0-600,$$$120,0-1000],[$$$115,600-1000,($no discount$)],[3,2500,$$$60,0-1000,$$$54,0-1500],[$$$56**,1000-2000,$$$52,1500-2500],[$$$51,2000-2500,],[$Total capacity $($units$),2500,2000]]$

$*$For example, if $1400$ units are purchased from Vendor $A,$ they cost $$56$ each, for a total of $$78,400.$

For the minimum$-$cost purchase plan for Universal, write the optimization model clearly with optimization model notation$($e$.$g$.$ objective function and constraints$)?$