# Stir R(x) = (500 – 10x)(5 + 0.15x)

Stir Sticks – PitchDescription of the Product: Flavored stir sticks made fromhard toffee, hard honey (candy), and frozen chocolate to spice up any drink!These tasty creations are made by freezing flavor over a Popsicle stick andpackaging in plastic wrappers.                 Goalfor Pitch: \$20,000 for 30% of the company. So far, we’ve been selling about \$500 items per month and onlooking at a profit of about \$4170 per month. It costs about an average of \$1.8to make each box and we sell it for \$8.35 in the current business plan. Business ModelCost Function: C(x) = mx, as the product is made from homeand thus far requires basic ingredients. The cost of each stick is roughly \$0.

80, with each Popsiclestick costing about \$0.05 and because we use high end products, the cost perflavor is about \$0.75 on average. Since we’re planning on buying in bulk, thecosts are significantly lowered the more we buy.

Each stick costs about \$1 topackage into the box \$0.80 + \$1 = \$1.8C(x) = 1.8xThe selling price would be \$5. For each \$0.15 increase in price, 10 less products will besold and the average sticks sold per month is 500. R(x) = (500 – 10x)(5 + 0.

15x)Note: x-axis is the price, and y-axis is the revenueRoots:R(x)        = (500 -10x)(5 + 0.15x)0              = (500 -10x)(5 + 0.15x)x = 500/10, x = 50x = -5/0.15, x = -33.

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3The roots of a revenue function represent the zeros and thenegative one is disregarded. This means that when the price is 50, \$0 revenuewill be made as no one will buy the product. Maximum:R(x)        = (500 -10x)(5 + 0.

15x)                = 2500+ 75x – 50x – 1.5×2                = 2500+ 25x – 1.5x2Max Revenue    =c-(b2/4a)                                =2500-(252/(4*-1.

5))                                =\$2604.2 when the price is \$8.33Domain: x ? 0Range: y ? 0The domain and range cut out the negative values (losses). New Revenue Function:R(x)        = (500 –10x)(8.33 + 0.

15x)                =4165 -75x +83.3x – 1.5×2                =4165 +8.

3x– 1.5x2Profit Function:P(x)        = R(x) –C(x)                = 4165 -8.3x– 1.5×2+1.

8x                              = 4165+ 8.3x – 3.3x2Note: x-axis is the selling price, and y-axis is the profitMaximum Profit: P(x)        = 4165 +8.3x – 3.

3x2Max Profit           =c-(b2/4a)                                =4165-(8.32/(4*-3.3))                                =\$4170.22  ReflectionsOur results were somewhat realistic; however the assumptionof at least 500 items being sold per month was a little optimistic.

I learnedhow important it is to do your research and know the customer demand beforedesigning a product or business plan. I also learned the correlation betweenprice and the profit is substantial because of the demand aspect. It wasdifficult to make the revenue functions and determine the price points.