Assignment:
Q1. Supply and Demand The supply function for a product is given by p=q²+2q+122 and the demand function for this product is p=650-30q, where p is the price in dollars and q is the number of hundreds of units. Find the price that gives market equilibrium and the equilibrium quantity.
Q2. Break-Even The weekly total cost function for a piece of equipment is C(x) =2000x+ 18,000+60x² dollars, and the weekly revenue is R(x) =4620x-12x²-x³, where x is the number of thousands of units. The x-values that are the solution to the system
y=2000x+18,000+60x²
y=4620x-12x²-x³
are the quantities that give break-even. Find these quantities.
Q3. Break-Evan The monthly total cost function for a product is C(x) =400x+0.1x²+17,901 dollars, and the monthly revenue is R(x) =1000x-0.01x², where x is the number of units. Find the numbers of units that’s give break-even for the product. (Hint: Use graphical methods to find one solution less than 100 units and one greater than 5000 units.)
Q4. Construction a Box A rectangular piece of cardboard with area 180 square inches is made in to an open box by cutting squares 2 inches on a side from each corner and turning up the sides. If the box is to have a volume of 176 cubic inches, what is the dimension of the original piece of cardboard?
Provide complete and step by step solution for the question and show calculations and use formulas.