Question

Here's the problem. Please help me solve or at least explain how to do it please.


The Toy Factory

Otto Toyom builds toy cars and toy trucks. Each car needs 4 wheels, 2 seats, and 1 gas tank. Each truck needs 6 wheels, 1 seat, and 3 gas tanks. His storeroom has 36 wheels, 14 seats, and 15 gas tanks. He needs to decide how many cars and trucks to build so he can maximize the amount of money he makes when he sells them. He makes $1.00 on each car and $1.00 on each truck he sells. (This is a very, very small business, but the ideas are similar for much larger enterprises.) We will divide t

Answer 1

We will divide this problem into subproblems.

a) Otto's first task is to figure out what his options are. For example, he could decide to make no cars and no trucks and just keep his supplies. On the other hand, because he likes to make trucks better, he may be thinking about making five trucks and one car. Would this be possible? Why or why not? What are all the possible numbers of cars and trucks he can build, given his limited supplies? This will be quite a long list. An easy way to keep your list organized and find some patterns is to plot the points that represent the pairs of numbers in your list directly on graph paper. Use the x–axis for cars and the y–axis for trucks. Make a fairly large, neat first quadrant graph. (Why the first quadrant?) We will need to use this graph later in this problem and in the next one.

Answer 2

We need to divide 36 wheels, 4 seats and 15 gas tanks
among
cars with 4 wheels, 2 seats and 1 gas tank
trucks with 4 wheels, 1 seat and 1 gas tank
to make the max number of vehicles

Answer 3

This might be a bit complicated, with simultaneous equations and such but
we only have 4 seats!

Answer 4

Do you see what to do?

Answer 5

Oh, 14 seats.

Answer 6

Not sure I can do what your teacher expects, but I notice that we can make a maximum of 5 trucks (6 wheels x 5 = 30, 5 seats, 15 gas tanks each) and no cars or
9 cars (4 wheels x 9 = 36, 18 seats, 9 gas tanks).

Answer 7

So I think the way to do this is to make a table with 6 entries,
#trucks from 0 to 5, calculate how many of each item are remaining, and then figure out how many cars you can make, then figure the total vehicles.

Or you can make a system of simultaneous equations. One of these other guys will probably jump in and show you that.

Answer 8

alrighty, thankyou so much.