1. The Mathematics Department has budgeted $59,728.35 to purchase whiteboard markers. They can purchase a box of assorted colors for $20.49 each and a box of black markers for $17.49 each from Office Depot.
a) Define your variables:
let x = __________________________ let y = __________________________
b) Write a linear equation to model the ways in which they might spend the money on tablets. Leave your equation in standard form: Ax + By = C
c) Find the x-intercept of your equation. Write your answer as a point.
d) Interpret the x-intercept in the context of this problem -- describe in words what it represents.
e) Find the y-intercept of your equation. Write your answer as a point.
f) Interpret the y-intercept in the context of this problem -- describe in words what it represents.
g) Find the slope of your equation. Write your answer as a fraction.
h) Interpret the slope in the context of this problem -- describe in words what it represents.
i) Choose a reasonable scale and graph the line.
2. A manufacturer can sell 400 watches for $11 each and 800 watches for $6 each.
a) Find a demand and price equation assuming the relationship is linear. p = D (q ) = _______________
b) Find the quantity demanded at $10 per watch.
c) Suppose the price and supply of the watch are related by p = S (q ) = .0075q , where p is the price in dollars and q is the number of watches supplied. Find the quantity supplied at $10 per watch.
d. Use algebra to find the equilibrium point and then graph both functions. Your graph should show y- intercepts and the equilibrium point clearly as well as any other points used to graph.
The equilibrium price is ____________ and the equilibrium quantity is ____________.
3. A taco stand can produce 10 dozen tacos for a cost of $70. The marginal cost per dozen is $5. They sell a dozen tacos for $15.
a) Write an equation for the cost assuming the relationship is linear. C (x ) = ____________
b) Write an equation for the revenue earned from selling the tacos. R (x ) = ____________
c) Use algebra to find the break-even point and then graph both functions. They will break even when making and selling __________
d) Find an equation for the profit function for making and selling x dozen tacos. P (x ) = ____________
e) What is the profit from making and selling 100 dozen tacos?
f) How many tacos will produce a profit of $500?