Math 103 Project 1
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School
California State University, Northridge *
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Course
130
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
5
Uploaded by ConstableKnowledge48961
Name: ______________________________ Math 103 Project 1
Part 1: A group of students from CSUN started a taco truck business called Matador Tacos. They need to figure out the price that they want to charge for each taco. After some research on some nearby taco truck businesses, the students were able to determine that the price-demand equation for their tacos is 0.1𝑥 + 5𝑝 = 40 where 𝑥
is the demand (in number of tacos) and 𝑝
is the price (in dollars) for each taco. They decided to sell them at different prices each week and compare the number of customers they receive depending on the price. 1.
Using the price demand equation, fill in the missing parts of the table below. p x $0.50 350 $1.50 225 2.
One of the students said, “
if we sell tacos at $1.75, we would sell 300 tacos
”
. Using the price-demand equation as evidence, do you agree with the student’s statement
? Explain why or why not.
3.
On one night the students decided to charge $2.00 per taco and were able to reach a demand of 370 tacos. Does this make sense based on the price-demand equation given? Provide a reason as to why this happened. Can a night like this happen and the taco business still have a price-demand equation of 0.1𝑥 + 5𝑝 = 40
? 4.
One of the students is interested in other price and demand options but writing them all down on a table can be very time-consuming. They decide to graph the possible values instead. Plot the points from question 1 on the price-demand graph below. Label price on the horizontal axis and demand on the vertical axis.
5.
Based on your graph, predict the intercepts. 6.
Find the intercepts using the price demand equation 0.1𝑥 + 5𝑝 = 40
. 7.
Interpret the intercepts. 8.
Find and interpret the slope of the line. 9.
Does it make sense to sell 800 tacos? Explain.
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Part 2: Since the students are just starting their business, they must rent a taco truck. The cost to rent the taco truck is $180 per week. They do not have to worry about paying workers since all the students decided to work for free until they can afford to buy their own taco truck. The only other thing they need to worry about is the cost of the ingredients per taco. The local supermarket wanted to help the students start their business so offered a 50% discount on all their ingredients (and food is not taxed). The receipt for ingredients to make 50 tacos (after the discount is applied) is given below: Tortillas $4.00 Meat $18.00 Cilantro $1.00 Onion $3.00 Salsa $5.00 10.
What is the cost per taco? 11.
Using question 10 and the cost of the truck rental, what is the formula for the weekly cost function? Hint: 𝐶(𝑥) = 𝐹 + 𝑉𝑥.
12.
The students anticipate that they will sell 200 tacos in their first week. a.
What is the cost to run the taco truck this week? b.
What price should students charge if they plan on having a demand of 200 tacos?
c.
Assume this is a cash-only business. If they were to sell all 200 tacos how much money would be in the register at the end of the week? (This is called the Revenue.) d.
How much profit did they make selling 200 tacos? (subtract your weekly cost from your revenue) 13.
One of the students thinks that selling more tacos next week will generate a higher profit. Let’s investigate
: Repeat the steps of number 12, but for 300 tacos. a.
What is the cost to run the taco truck this week? b.
What price should students charge if they plan on having a demand of 300 tacos? c.
Assume this is a cash-only business. If they were to sell all 300 tacos how much money would be in the register at the end of the week? (This is called the Revenue) d.
How much profit did they make selling 300 tacos? (subtract your weekly cost from your revenue) 14.
Did they make more of a profit selling 200 or 300 tacos?