Show all of your work including any arithmetic steps. Calculator instructions are given on each problem. 1) A dog food company sells two kinds of dog food: grain-free and soy-based. The demand functions are p= 75 - 0.18x - 0.05y (10 pts) q=61 - 0.03x - 0.22y, where x is the number of bags of grain-free food sold weekly, and p is the demand function for grain-free, and y is the number of bags of soy-based food sold weekly, and q is the demand function for soy-based. The cost of manufacturing one bag of grain-free food is $10.50, and the cost of manufacturing one bag of soy-based food is $13.20. Find the price to charge for each type of food to maximize profit. Show all your work, and use a calculator for the arithmetic. 2) Find this definite integral. Show work. Use a calculator for the exponentials and the arithmetic. (10 pts) 12 5 xe-0.12x dx