Question

Medal! Help please?

A dealer has a lot that can hold 30 vehicles. In this lot, there are two available models, A and B. The dealer normally sells at least twice as many model A cars as model B cars. If the dealer makes a profit of $1300 on model A cars and $1700 on model B cars, how many of each car should the dealer have in the lot given that the total profit for the sale of both cars is $43,000?

Answer 1

a.
20 model A
10 model B

b.
10 model A
20 model B

c.
5 model A
25 model B

d.
16 model A
14 model B

Answer 2

Oh, and I know that the answer is not B.

Answer 3

I just went through and plugged all of the numbers into their given prices and got A.
Model A: 1300(20) = 26000
Model B: 1700(10) = 17000
26000+17000= 43,000

but how would I create the equation/inequality to solve for this answer?

Answer 4

A + B <= 30 seems to be missing.

Answer 5

You might need A = 2B in there, but I'm a little worried about this one with the negative sign. What do we know of slack variables?

Answer 6

Slack variables?

Answer 7

You'll meet them later, perhaps. For now, let's not worry about it.

A = 2B results in A - 2B = 0. That should be a little unsettling as you may not have used "=" in this sort of a problem.

Answer 8

Mkay, I following you.

Answer 9

Collect the stuff we've been looking at...

A + B <= 30
A - 2B = 0

Maximize: 1300A + 1700B

OR, since it's really the same problem, figure out how to get $43,000 out of the deal.

a, b, c, and d all add up to 30, so that doesn't clear anything out.
There is only one, a, where A = 2B. That may just be the solution.