Problems 1 through 4: Regina’s Jewelry Regina has a hobby of making jewelry by hand and would like to turn her passion into a business.  She plans to sell her work on an e-commerce website, but she wants to make sure that she is being efficient with her time and does not produce too many or too few pieces. 
Problem 1 (Related Exercises: Section 1.3 #1, 4, and 5) Each month, Regina is going to make 30 pieces of jewelry for fun, even if she does not sell any of them.  She is willing to make one additional piece each month for every $5 that the selling price increases.  This determines the following supply function: 
𝑆(𝑝) = 30 + 0.2𝑝 
Determine the slope and y-intercept of this line.  In addition, explain how someone would determine this supply function using the information provided about Regina’s business. 
Problem 2 (Related Exercises: Section 1.3 #7)  Regina does some research to see how other online jewelry retailers perform.  She finds two retailers who make similar jewelry: one retailer sells a quantity of 48 pieces per month at a price of $30, and the other sells a quantity of 41 pieces per month at a price of $100.  Use this information to write a linear equation that models the quantity demanded as a function of price. 
𝑞 = 𝐷(𝑝) 
Problem 3 (Related Exercises: Section 1.3 #9 and 13) Illustrate the supply function from problem 1 and the demand function from problem 2 in a single graph.  Your graph should contain the following: • A label indicating what each axis represents • The supply function, labeled S(p) • The demand function, labeled D(p) • An indication of the equilibrium point 
Problem 4 (Related Exercises: Section 1.3 #13) Based on the information provided, how many pieces should Regina make each month, and at what price should she sell each piece to achieve equilibrium?  Explain how you determined your answers.