Chain Rule Part III Pedro manages a gas station that sells two kinds of gum, brand A and brand B. Analysts have estimated that if brand A is sold for pA dollars and brand B for pg dollars, then demand for brand A will be: Q% = 300 - 20(PA + 1)2 + 30pg bottles per month (1.2) Furthermore, research indicates that the price of both brands is a function of time t, where t is measured in months. In particular, the price of brand A in t months is PA(t) = 2 +0.05t dollars per bottle (1.3) 14 1 Math Review whereas the price of brand B in t months will be PB(t) = 2 +Vf dollars per bottleQuestions 1. Compute botha xand aQ B.oth functions should be functions of t. In words, describe what your partial derivative functions model. 2. At what rate should Pedro expect the demand for gum to be changing with respect to time (i.e. %) 4 months from now? Should he expect demand to be increasing or decreasing at that time? 3. Which brand price grows fastest? Describe that range of time t that a brand price is growing faster than the other (e.g. Brand A grows faster for t :1 3 months). 4. Does brand A function as complement or substitute good? How do you know