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Here n represents the number of items produced. Use this formula to determine the cost associated with producing n = 100 units, C = 62(100) + 5,280 = 11,480 Therefore, the cost associated with producing 100 items is $11,480. Profit is revenue less costs, Profit Revenue - Cost = 15,000- 11,480 = 3.520

Here n represents the number of items produced. Use this formula to determine the cost associated with producing n = 100 units, C = 62(100) + 5,280 = 11,480 Therefore, the cost associated with producing 100 items is $11,480. Profit is revenue less costs, Profit Revenue - Cost = 15,000- 11,480 = 3.520

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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This equation shows that the profit generated by producing and selling 100 items is $3,520. In general, given a revenue formulaR and a cost formula, Owe can form a profit function by subtracting as follows: P-R-C Example: The cost in dollars of producing n items is given by the formula C = 62n +5280. The revenue in dollars is given by R = 150n where n represents the number items sold. Write a formula that gives the profit generated by producing and selling n items. Use the formula to determine how many items must be produced and sold to earn at least $7,000 in profit. Solution: Obtain the profit function by subtracting the cost function from the revenue function. PR-C = 150m (62n +5,280) = 150n62n-5, 280 = 88n-5, 280 Therefore, P = 88n - 5, 280 models the profit. To determine the number of items that must be produced and sold to profit at least $7,000 solve the following: P27,000 885, 2807,000 887212, 280 n2 139.5 Round up because the number of units produced and sold must be an integer. To see this, calculate the profit when n is 139 and 140 units. P = 88(139)-5, 280 = 6,952 P = 88 (140) -5,280 = 7, 040 Answer: 140 or more items must be produced and sold to profit at least $7,000. Sometimes the costs exceed the revenue, in which case, the profit will be negative. For
Transcribed Image Text:This equation shows that the profit generated by producing and selling 100 items is $3,520. In general, given a revenue formulaR and a cost formula, Owe can form a profit function by subtracting as follows: P-R-C Example: The cost in dollars of producing n items is given by the formula C = 62n +5280. The revenue in dollars is given by R = 150n where n represents the number items sold. Write a formula that gives the profit generated by producing and selling n items. Use the formula to determine how many items must be produced and sold to earn at least $7,000 in profit. Solution: Obtain the profit function by subtracting the cost function from the revenue function. PR-C = 150m (62n +5,280) = 150n62n-5, 280 = 88n-5, 280 Therefore, P = 88n - 5, 280 models the profit. To determine the number of items that must be produced and sold to profit at least $7,000 solve the following: P27,000 885, 2807,000 887212, 280 n2 139.5 Round up because the number of units produced and sold must be an integer. To see this, calculate the profit when n is 139 and 140 units. P = 88(139)-5, 280 = 6,952 P = 88 (140) -5,280 = 7, 040 Answer: 140 or more items must be produced and sold to profit at least $7,000. Sometimes the costs exceed the revenue, in which case, the profit will be negative. For
In a business application, revenue results from the sale of a number of items. For example, if an item can be sold for $150 and we let n represent the number of units sold, then we can form the following revenue function: R = 150m Use this formula to determine the revenue generated from selling units, R = 150(100) = 15,000 Therefore, the revenue generated from selling 100 items is $15,000. Typically, selling items does not represent the entire story. There are a number of costs associated with the generation of revenue. For example, if there is a one-time set-up fee of $5,280 and each item costs $62 to produce, then we can form the following cost function: C = 62n +5,280 Here n represents the number of items produced. Use this formula to determine the cost associated with producing n = 100 units, C = 62(100) + 5,280 = 11,480 Therefore, the cost associated with producing 100 items is $11,480. Profit is revenue less costs, Profit Revenue - Cost = 15,000 11, 480 = 3,520
Transcribed Image Text:In a business application, revenue results from the sale of a number of items. For example, if an item can be sold for $150 and we let n represent the number of units sold, then we can form the following revenue function: R = 150m Use this formula to determine the revenue generated from selling units, R = 150(100) = 15,000 Therefore, the revenue generated from selling 100 items is $15,000. Typically, selling items does not represent the entire story. There are a number of costs associated with the generation of revenue. For example, if there is a one-time set-up fee of $5,280 and each item costs $62 to produce, then we can form the following cost function: C = 62n +5,280 Here n represents the number of items produced. Use this formula to determine the cost associated with producing n = 100 units, C = 62(100) + 5,280 = 11,480 Therefore, the cost associated with producing 100 items is $11,480. Profit is revenue less costs, Profit Revenue - Cost = 15,000 11, 480 = 3,520
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