(a) Write the differential equation given by the Evans price adjustment model for the price p as a function of time. (Use k for the constant of proportionality.)   dp/dt=k   (c) Find the particular solution in which Eggbert dolls are initially priced at $10 and the price rises to $12 after one month. p(t)=

Yaster Breakfast Supplies is planning to manufacture and market a new toaster. After conducting extensive market surveys, the research department provides the following estimates: • a weekly demand of 318 at a price of $13 per toaster • a weekly demand of 201 at a price of $16 per toaster The financial department estimates that weekly fixed costs will be $1,399 and variable costs (cost per unit) will be $3. Assume: • the relationship between price and demand is linear • the cost function in linear Use your models to predict the marginal profit when Yaster is producing and selling 271 toasters per week. Round to the nearest cent. $ per toaster