$10.$ Deriving demand from an indifference map

Deborah recently m$$ved to Dallas, where they developed a taste for drinking Americaneas and eating danishes. Assume throughout this problem that the price of an Americans is held constant at $\backslash (\backslash$$ $3\backslash ).$

On the following graph, the purple ourves $(\backslash (\backslash$mathrm$\{$I$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$I$\}\_\{2\}\backslash ))$ describe two of Deborat's indflerence curves. The lines $\backslash (\backslash$mathrm$\{$BC$\}\_\{1\}\backslash )$ and $\backslash (\backslash$mathrm$\{$BC$\}\backslash$mathrm$\{$C$\}\_\{2\}\backslash )$ represent tes budget constraints. Points X and $\backslash ($ Y $\backslash )$ show Deborah's optimal consumption bunales subjedt to the budget constraints.

Given the probeding graph and knowing the price of an Americano is $\backslash (\backslash$$ $3\backslash ),$ Deborah's avalable income for Americanos and danishes it

following graph.

Hint: Assume that Deborah's demand for darishes ia a straight line. You should derive two points on the demand ourve from the preceding graph. Then place the blue line on the folowing graph so that it passes through these two points.