Angela spends all her money on magnetometers and food. Her preferences are given by , such that her marginal utility of magnetometers is , and her marginal utility of food is. Angela has $100 to spend on magnetometers and food, and a magnetometer costs $2 per unit, while food costs $1 per unit.
a. Write down the equation Angela's budget constraint for food and magnetometers.
b. What is Angela's marginal rate of transformation (MRT)?
c. What is Angela's marginal rate of substitution (MRS)? Hint: make sure that the x-variable is the same for the MRT in part (b) as for MRS in part (c).
d. Compute the optimal amount of magnetometers and food Angela will buy.