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Sunny_sXe [5.5K]
3 years ago
14

The profit that the vendor makes per day by selling x pretzels is given by the function. P(x) = -0.002x2 + 1.4x - 400. Find the

number of pretzels that must be sold to maximize profit.
Business
1 answer:
amm18123 years ago
7 0

Answer:

350 the number of pretzels that must be sold to maximize profit.

Explanation:

P(x) = -0.002x2 + 1.4x - 400

Differentiating P(x) with respect to dx:

P(x)'=\frac{d(-0.002x2 + 1.4x - 400)}{dx}

P(x)'=-2\times 0.002x+1.4

Putting , P(x)' =0

0=-0.004x+1.4

x=\frac{1.4}{0.004}=350

we get , x = 350

Differentiating P(x)' with respect to dx:

P(x)''=-0.004

P(x)''<0 (maxima)

350 the number of pretzels that must be sold to maximize profit.

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D) PV= 6600/0.05= $132,000

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1-a. Dollars of gross profit from selling tags = $9,180

1-b. Dollars of gross profit from selling cases = $1,500

1-c. Gross profit percentage from selling tags = 72.86%

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1. Calculate the dollars of gross profit and the gross profit percentage from selling tags and cases.

2. Which product line yields more dollars of profit? - Which product line yields more profit per dollar of sales?

The explanation of the answers is now given as follows:

1. Calculate the dollars of gross profit and the gross profit percentage from selling tags and cases.

Sales revenue from tags = Sales value of 160 tags mailed to customers on Jan. 8 at a price of $30 per tag + Sales value of 260 tags mailed to customers on Jan. 21 at a price of $30 per tag = (160 * $30) + (260 * $30) = $12,600

Sales revenue from cases = Sales value of 120 cases mailed to customers on Jan. 19 at a price of $15 per case = 120 * $15 = $1,800

Total number of tags sold = 160 tags mailed to customers + 260 tags mailed to customers on Jan. 21 = 420

Total number of cases sold = 120 cases mailed to customers on Jan. 19 at a price of $15 per case = 120

Using FIFO, we have:

Cost of tags sold = Value of 260 tags purchased on Jan.2 from Xioasi Manufacturing (XM) at a cost of $7 per tag + Value of the remaining 160 (i.e. 420 – 260 = 160) tags sold based on the 360 tags purchased on Jan. 11 from XM at a cost of $10 per tag = (260 * $7) + (160 * $10) = $3,420

Cost of cases sold = Value of 60 cases purchased on Jan.4 from Bachittar Products (BP) at a cost of $2 per case + Value of the remaining 60 cases sold based on the 160 cases purchased on Jan. 14 from BP at a cost of $3 per case = (60 * $2) + (60 * $3) = $300

Therefore, we have:

1-a. Dollars of gross profit from selling tags = Sales revenue from tags - Cost of tags sold = $12,600 - $3,420 = $9,180

1-b. Dollars of gross profit from selling cases = Sales revenue from cases - Cost of cases sold = $1,800 - $300 = $1,500

1-c. Gross profit percentage from selling tags = (Dollars of gross profit from selling tags / Sales revenue from tags) * 100 = ($9,180 / $12,600) * 100 = 72.86%

1.d. Gross profit percentage from selling cases = (Dollars of gross profit from selling cases / Sales revenue from cases) * 100 = 83.33%

2. Which product line yields more dollars of profit? - Which product line yields more profit per dollar of sales?

2-a. Which product line yields more dollars of profit?

From part 1 above, we have:

Dollars of gross profit from selling tags = $9,180

Dollars of gross profit from selling cases = $1,500

Since the dollars of gross profit from selling tags of $9,180 is greater than the dollars of gross profit from selling cases of $1,500, this implies that Tag yields more dollars of profit.

2-b. Which product line yields more profit per dollar of sales?

From part 1 above, we have:

Total number of tags sold = 420

Total number of cases sold = 120

Therefore, we have:

Tag's profit per dollar of sales = Dollars of gross profit from selling tags / Total number of tags sold = $9,180 / 420 = $21.86

Case's profit per dollar of sales = Dollars of gross profit from selling cases / Total number of cases sold = $1,500 / 120 = $12.50

Since Tag's profit per dollar of sales of $21.86 is greater than Case's profit per dollar of sales of $12.50, this implies that Tag yields more profit per dollar of sales.

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