[hansthak]

ABC company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that ABC can increase sales by 12000units for each $3 reduction in the selling price. The comp. Present selling price is $70per unit, variable cost $40per unit, fixed exp. $450000 per year. The present annual sales volume is $25000 units.

A. What is the present yearly operating income or loss?
B. What is the present breakeven point in unit and in dollar sales?
C. Assuming that the marketing studies are correct what is the max. Operating income that ABC can earn yearly?
D. At how many units and at what selling price per unit would ABC generate the operating income you determined in (C) .

[ArcSine]

(A) is pretty straightforward. What have you come up with, and why do you think it's wrong?

As a hint for (B), first determine the BE point in units. You can get that number quickly by dividing the total fixed costs by the current unit profit margin (which is the current unit selling price, less the unit variable cost). Then the BE point in terms of dollar sales immediately follows, using 70 as the unit selling price.

To attack (C) and (D), first develop a function which gives the number of units sold Q in terms of selling price P. The supplied information suggests it's linear, with a slope of +12,000/(-3) = -4,000.

From that linear Q(P) function you can develop a net profit function, using the fact that Revenue will be Quantity x Price; total variable costs will be Quantity x unit variable cost; and Fixed Costs are just a constant, as given.

Your resulting profit (as a function of unit price P) will be a concave quadratic. From there, you can determine the max profit either algebraically (by finding the vertex of that quadratic), or by finding the unique point at which the quadratic's first derivative equals zero.

Either way, you'll have the price at which profit is maximized. Take that result back to your original Q(P) function to see the corresponding quantity.

[hansthak]

So, I tried to solve this question using the same guidelines u gave me. Could you please see if I got this correct? Please

Question:
ABC company introduced a new product last year for which it is trying to find an optimal selling price. Marketing studies suggest that ABC can increase sales by 8000units for each $8 reduction in the selling price. The comp. present selling price is $80per unit, variable cost $60per unit, fixed exp. $400000 per year. The present annual sales volume is $35000 units.

A. What is the present yearly operating income or loss?
- I got $300,000

B. What is the present breakeven point in unit and in dollar sales?
- I got breakeven point = 20,000 units
- sales is $1,600,000

C. Assuming that the marketing studies are correct what is the max. operating income that ABC can earn yearly?
- I got maximum operating income as 300,000

D. At how many units and at what selling price per unit would ABC generate the operating income you determined in (C) .
- I got max operating income occurs at 35000 units and $80/unit

E. what would be the breakeven and sales dollars using the selling price determined in (d)?
- I got breakeven point as 20000 units and 1,600,000 in sales $

Please let me know if this is correct..

thanks

[ArcSine]

You nailed A and B; nice work.

On C, D, and E, though, you missed the mark. The company's profit isn't maxed at their current output level.

The first step is to write up a formula that gives the company's total sales, in units, for any given unit sales price. It will be of the form

Total units sold = (some slope) x (unit price), plus (some constant)

This just corresponds to the familiar y = mx + b generic linear function, with total units sold playing the role of y, slope = m, x = unit price, and b is the constant.

You're given two facts which make it possible to derive this formula: First we know that the "sensitivity" of sales to price is that for every $8 drop in unit price, customers will buy 8,000 more units. This tells you that the slope of this equation which we're trying to derive is +8,000 / -8 = -1,000.

So far, then, our formula looks like Q = -1,000P + (some constant). (I'm using Q and P for quantity and unit price, instead of the generic y and x.)

To figure out the constant, you can then use our second known fact: at a unit price of 80, these guys are selling 35,000 units. In other words, you want to come up with the equation for a line, and you've been given the slope and a single point on the line.

So start by giving me the completed formula. All you need to do at this point is replace (some constant) by a particular number.

[maidahinlo]

Hi,
I am working on the related problem above. For the above, the equation would be :

80+ (-1000)P. This would be the same formula for Marginal Revenue? Is this right?

What would be the next step? I've read that profit is maximized if MR=MC. How does this relate to the problem above?

Thanks in advance.