Hickory Company manufactures two products $-13,000$ units of Product $Y$ and $5,000$ units of Product $Z.$ The company uses a plantwide overhead rate based on direct labor$-$hours. It is considering implementing an activity$-$based costing $($ABC$)$ system that allocates all $$788,400$ of its manufacturing overhead to four cost pools. The following additional information is available for the company as a whole and for Products $Y$ and $Z$ :

$\backslash$table$[[,,$Estimated Overhead,$],[$Activity Cost Pool,Activity Measure,Cost,Expected Activity$],[$Machining$,$Machine$-$hours,$$238,800,12,000$ MHs$],[$Machine setups,Number of setups,$$93,100,190$ setups$],[$Product design,Number of products,$$83,000,2$ products$],[$General factory,Direct labor$-$hours,$$373,500,14,400$ DLHs$]]$

$\backslash$table$[[$Activity Measure,Product Y$,$Product Z$],[$Machine$-$hours,$6,900,5,100],[$Number of setups,$40,150],[$Number of products,$1,1],[$Direct labor$-$hours,$7,900,6,500]]$

Using the ABC system, what percentage of the Product Design cost is assigned to Product $Y$ and Prodict $Z?$

$\backslash$table$[[,$Product $Y,$Product Z$],[$Product design cost,$\%,\%$