In 2005, Americans bought 9.1 million home radios and 3.8 million home-theater-in-a-box units (TWICE, March 27, 2006, www. twice/article/CA6319031.html). Suppose (for simplicity) that the cost of the home radios was $230 million, that the cost of the home-theater-in-a-box units was $770 million, and that the average consumer has a Cobb-Douglas utility function and buys only these two goods. Estimate a plausible Cobb-Douglas utility function such that the consumer would allocate income in the proportions actually observed. The typical consumer's Cobb-Douglas utility function, where R is radios and T is home-theater-in-a-box units, is U(R, T)equals nothing. (Enter the exponents in your equation rounded to two decimal places.) (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E. g., a superscript can be created with the ^ character.)