# Thread: Profit while units remain constant

1. ## Profit while units remain constant

Can anyone help me solve this problem and show me how it's done? I need it for a work seminar and am stuck in the sand

Your Goal is to grow your profit dollars by 10% next year, but you expect no growth in unit sales. Based on this year's results shown below, assuming no changes in retail price or cost, how many units must you shift from standard products to premium products in order to achieve your goal?

...........................Units...............Dol lars........................Profit Dollars
Premium Products 706,425 ........... 6,285,400................. 2,543,130
Standard Products 625,000.............3,678,700.................. 825,000
Total Products 1,331,425...........9,964,100...................3, 368,130

2. ## Re: Profit while units remain constant

First calculate the profit per unit for both the standard and premium product lines; let's call these values P_s for "profit per unit on standard product" and P_p for profit/unit on premium product. The total profit is then:

$P_s \times Q_s + P_p \times Q_p = Total\ Profit$

Now you want to change the quanties of standard and premium products sold, but keep the total volume the same. Let 'x' = increase in number of premium products sold, so the new quantity of premium products is Q_p+x. That means the new number of standard products sold is Q_s-x. The total profit is increased 10%, so now you have the new equation:

$P_s(Q_s-x) + P_p(Q_p+x) = 1.1 \times Total\ Profit$

Solve for x.