I've been trying for a while! Please solve with steps it's due today
November 14 Wor shop for Math 151 1. A child waats to build a tunnel using thre identical boards, each 4 feet wide, one for the top and one for each side as shown. The two sides are to be tilted at equal angles θ to the floor What is the maximum cross-sectional area A that can be 4 feet 4 feet FLOOR 2 Economists often use utility functions to messure a person's happiness. Lets say thst Reggie is going to the grocery store with $100 to stock up on peanut butter and jelly for the year. His utility function is given by ãa where p represents the number of cans of peanut butter he purchases and j the number of cans of jelly he purehases (a) Assume that cans of peanut butter cost $1 as do cans of yelly. Rewrite U(p.)sa function of j (b) How many cans of jelly should Reggle parchase in order to maximize his utility? (Note It would be correct to assume he can only purchase & whole number of both cans of PB and cans of jelly) (e) Say the store is running a specal, where i a customer purchases fifty cans of peanut butter they receive ten for free. How may cans of jelly should Resgie purchase in this s utilty as a function of one variable, it should be written ssa piecewise fuaction depending on whetber Sfty or more cans of situation? (Hint When one rewrites Reggie' peanut butter were purchased.) the area under the function+2 on the interval [1,3 using 4 rect angles. (Whlchever type you feel like using 4. Define %(n)s 16 + 26 + 3s + . . . + ns (agammation notation, s In-Σ ks). An explicit formula for Se(n) is known, and it is: Assume that this formula is true.
