Math 1100-006 Quiz 1 2 September, 2011 Answer the questions in the spaces provided. If you run out of room for an answer, you may continue on the back. Show all of your work. Round answers as appropriate (dollar amounts to the nearest penny, and quantities to whole numbers where logical). Solution Key 1. (10 points) Fred’s company makes widgets, and sets the price p in dollars using the formula 100eq p= q+1 where q is the number of hundreds of units produced. What will the price be when 100 units are produced? Solution: When 100 units are produced, q = 1. Substitute this into the equation for p and simplify to get: 100e1 1+1 100(2.71...) = 2 = 135.50 p= So the price will be approximately $135.50 when 100 widgets are produced. 2. (10 points) The demand function for widgets is given by p = 100e−q/2 where p is the price, in dollars, when q units are demanded. If the price is $1.83 per widget, how many widgets will be demanded? (Assume that only whole widgets are possible.) Solution: To find the demand when the price is $1.83 per widget, we need to solve for q in the equation below: 1.83 = 100e −q 2 −q 0.0183 = e 2 −q ln(0.0183) = 2 q = −2 ln(0.0183) ≈ 8 So approximately 8 widgets are produced in order for the price to be $1.83.