I am having trouble doing the part c ,d , e and f

PHYS100 - HW4 Due: Wednesday, January 29 (at the beginning of lecture) You must show all of your work in order to receive full credit. 1) Suppose you and few partners decide to start an organic, cruelty-free, fair-trade t-shirt company. In order to ensure that your business succeeds, you hire an independent business consultant to do research on the current t-shirt market. They find that the mumber of t-shirts you could sell each month is a linear function of cost per shirt. They predict your monthly t-shirt sales to be 1750 shirts if you price them at $15.25 per shirt or 791 shirts if you price them at $21.75 per shirt. la) (10 points) Write a linear equation expressing the number of t-shirts sold each month as a function of price per t-shirt. Please be explicit about what your chosen variables represent. Find the slope and intercepts of this equation (including their units). What real life meaning do these values have? Please show ALL of the work you did to calculate these values. lb) (5 points) Neatly plot your linear equation from la on a Cartesian plane (with appropriate axes, labels, and scales). Be sure to label the two coordinate pairs given in the question prompt as well as the two intercepts from la on your line. +5 bonus points if you make this graph (with labels and labeled coordinate pairs) in Excel (which is included with Drezel's Office 365 subscription). lc) (2.5 points) Write the quadratic equation that expresses your monthly revenue/sales (measured in $) as a function of price per t-shirt. Please be explicit about what your chosen variables represent. Hint: In part la, you found an equation that calculates the number of t-shirts you'lu sell each month based on your t-shirt price. ld) (2.5 points) Your company has a fixed monthly operating cost of $4173 (rent, fixed utilities, etc.) on top of the $5.13 it costs you to make each t-shirt. Write a linear equation expressing your total monthly expenditures/costs as a function of price per t-shirt. Again, please be explicit about what your chosen vari- ables represent. le) (15 points) Your monthly profits are found by subtracting your monthly expenditures/costs from your monthly revenues/sales. Express your monthly profits as a function of price per t-shirt. What do these values represent in the context of this problem? Please show ALL of the work you did to calculate these values. 1f) (5 points) In order to maximize your monthly profits, at what price should you sell your t-shirts? How did you come to this conclusion? If you sell your t-shirts at this price, how many shirts will you sell in a month? What will your monthly profits be if you sell your t-shirts at this price