Minnesota Shipping Services is planning to spend $8316000 on new vehicles for its fleet. They are planning on purchasing a combination of cars that cost $25200 each, vans that cost $34400, and small trucks that cost $48000. In addition, a recent needs assessment indicated that they should purchase 3 times as many vans as small trucks. General question: How many of each type of vehicle should be purchased while using up the entire budget? Set up a system of equations, and then solve using your calculator. a) There are actually an infinite number of solutions to this system. Write the solutions here, using tt as the parameter as needed. Solution: x= _______ cars ; y= _______ vans ; and z= _______ small trucks. b) How many of the infinite solutions are actually realistic for this problem? {Show your work as to HOW you got the answer.} _________ realistic solutions c) Which specific solution to this problem gives the largest number of cars for the fleet? ie, How many of each type of vehicle should be purchased in order to get the largest number of cars for the fleet? _____ cars, ______ vans, and _______ small trucks should be purchased.
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Minnesota Shipping Services is planning to spend $8316000 on new vehicles for its fleet. They are planning on purchasing a combination of cars that cost $25200 each, vans that cost $34400, and small trucks that cost $48000. In addition, a recent needs assessment indicated that they should purchase 3 times as many vans as small trucks. General question: How many of each type of vehicle should be purchased while using up the entire budget? Set up a system of equations, and then solve using your calculator.
a) There are actually an infinite number of solutions to this system. Write the solutions here, using tt as the parameter as needed. Solution:
x= _______ cars ;
y= _______ vans ; and
z= _______ small trucks.
b) How many of the infinite solutions are actually realistic for this problem? {Show your work as to HOW you got the answer.}
_________ realistic solutions
c) Which specific solution to this problem gives the largest number of cars for the fleet? ie, How many of each type of vehicle should be purchased in order to get the largest number of cars for the fleet?
_____ cars, ______ vans, and _______ small trucks should be purchased.
d)How many of each type of vehicle should be purchased in order to get the fewest number of total vehicles for the fleet?
_______ cars, _______ vans, and ________ small trucks should be purchased.
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