Suppose that Omar's marginal utility for cups of coffee is constant at $4\mathrm{.}5$ utils per cup no matter how many cups he drinks. On the other hand, his marginal utility per doughnut is $11$ for the first doughnut he eats, $10$ for the second he eats, $9$ for the third he eats, and so on $($that is$,$ declining by $1$ util per additional doughnut$).$ In addition, suppose that coffee costs $$1$ per cup, doughnuts cost $$1$ each, and Omar has a budget that he can spend only on doughnuts, coffee, or both. How big would that budget have to be before he would spend a dollar buying a first cup of coffee?

Instructions: Enter your answer as a whole number.