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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...

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?

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Q1a) let x = number of box of assorted colour and y= number of box of black markers
b) $20.49x + $17.49y = $59728.35
c) y = mx + c
$17.49y = -$20.49x + $59728.35
X-intercept corresponds to the...

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