Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 200 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 400 per week at $2 per shirt. (a) On the basis of this information, construct a linear demand equation for Yoda vs. Alien T-shirts. Hence obtain the weekly revenue R as a function of the unit price x. R(x) = (b) The university administration charges the fraternities a weekly fee of $300 for use of the student center. Write down the weekly profit P as a function of the unit price x. HINT [See Example 4.] P(x) = Determine how much the fraternities should charge to obtain the largest possible weekly profit. x = $ per T-shirt What is the largest possible weekly profit? $
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
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Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Two fraternities, Sig Ep and Ep Sig, plan to raise money jointly to benefit homeless people on Long Island. They will sell Yoda vs. Alien T-shirts in the student center, but are not sure how much to charge. Sig Ep treasurer Augustus recalls that they once sold 200 shirts in a week at $6 per shirt, but Ep Sig treasurer Julius has solid research indicating that it is possible to sell 400 per week at $2 per shirt.
| R(x) = |
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(b) The university administration charges the fraternities a weekly fee of $300 for use of the student center. Write down the weekly profit P as a function of the unit price x. HINT [See Example 4.]
| P(x) = |
|
Determine how much the fraternities should charge to obtain the largest possible weekly profit.
x = $ per T-shirt
What is the largest possible weekly profit?
$
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