Math Question Help

Question

Hi guys,

Can anyone assist with these two questions?

1.A firm produces widgets at a cost of C per unit, has a fixed overhead cost of F, and can sell each widget it makes at a price of P per unit. With Q representing the number of widgets made and sold, write a mathematical expression for the firm's profit as a function of Q. Write the mathematical expression for the break-even quantity. (in other words, solve for the value of Q, in terms of C, F, and P, which will make profit equal to zero.)

2.The function MAX(.,.) reports the larger of the two entries in the parentheses. For example, MAX(4,7)=7. Let y=MAX(5,x-20) and graph y as a function of x.

Any help is much appreciated!

VeritasPrepDennis · Answer

amajor99 -

While I am not sure that these are GMAT questions, here goes:

1. The goal is to set up an equation for the Break-Even Quantity. The break even is the Profit from selling the widgets (the Revenue of the widgets minus the Cost to produce the widgets) that is equal to the Fixed Cost. The Revenue of the Widgets sold can be expressed as QP ( the quantity sold time the price of each widget sold); the Cost to Produce can be expressed and QC ( the quantity sold time the cost of each widget to produce); the Profit, therefore, can be expressed as QP - QC. Setting the Profit equal to the Fixed Costs gives us the Break-even, so QP -QC = F. Now, the question asks us to solve for Q, so we can re-write the algebraic expression as: Q(P-C) = F. We can further manipulate the expression by dividing both sides by Q ==> (P-C) = F/Q and even further still, by dividing both sides by F ==> (P-C)/F = Q. This tells us that the Profit per widget divided into the Fixed Costs will give us the Break-even Quantity of Widgets to produce and sell.

2. This one is easy. Simply begin plugging values in for x (-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5) and determine the y values based on the Function. Create your x, y pairs and graph. I am not sure how a question like this would be asked on the GMAT, however.

amajor99 · Answer

thank you!

VeritasPrepDennis · Answer

amajor99 -

You are welcome.
Out of curiosity, can you post the GMAT questions these came from? I am interested in seeing how these questions are structured. Thanks.

amajor99 · Answer

They are actually from a problem set my program provided to work on before school starts.

VeritasPrepDennis · Answer

amajor99 -

Ok, thanks. I was having a hard time envisioning how #2 might be asked on the GMAY. Good luck!

ENGRTOMBA2018 · Answer

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