Im not sure how to do 2.b)

Notes: OGCU TS. In the questions belowr we will measure time t during the year in months with t=0 the beginning of the year (Western calendar) January 1 just after midnight) and t=12 the end of the year (December 31 just before midnight). (tidbit) Doctor Roberts sets up a factory producing Cherry Blossom Widgets (CBW). This factory is the only producer (monopoly). The fixed costs of the factory are $7,000 per month and the price to produce a CBW is $4. A market study done at a particular time of year predicts that the demand q(p) tor CBW is qtp)=50-p where q is the demand in thousands of CBW per month when p is the sale price in dollars. Let x be the factory production in thousands of CBW per month that meets demand at price p. a)(t mark) Write the cost function (30:) in thousands of dollars per month. b)(1 mark) Write the revenue function R(x) in thousands of dollars per month. c)(1 mark) Write the profit function Pix) in thousands of dollars per month. d)(1 mark) Determine the optimal profit per month and the production level at which it Give units for your answers. (2 marks) (*i'it'?) Doctor Roberts notices that the demand for CBW is not constant during the year. It is highest in the Spring (t=3) and lowest in the Fall (t=9). A consulting firm. Math Knights Inc., is hired and they predict a time-dependent demand curve of the form q{p)=(1+Asin{ntf6))(50-p). with A a constant in the interval (0. 1) that they estimate to be A=1r4 using market research. a)(2 marks) Describe briefly why the form of the demand model is reasonable in its behaviour in t and p. b)(2 marks) At what times of the year could the market survey from question #2 have been done? c)(4 marks) If the CBW production is fixed at x=20 (20,000 widgets per month) and the price adjusted over time to the demand curve, what is the rate of change of revenue with respect to time on February 1 (t=1)? Make sure to give units to your