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If the daily cost per unit of producing a product by the Ace Company is 20 + 0.2x dollars, and if the price on the competitive market is $70, what is the maximum daily profit the Ace Company can expect on this product?

I got $125. If someone could please explain what I did wrong I'd appreciate it.

User DFriend
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2 Answers

6 votes

Final answer:

The maximum daily profit the Ace Company can expect on this product is $17,430. To find the maximum profit, you need to set the revenue per unit equal to the cost per unit and solve for the number of units produced. By substituting this value into the profit equation, you can calculate the maximum daily profit.

Step-by-step explanation:

To find the maximum daily profit, we need to calculate the cost per unit and the revenue per unit. The daily cost per unit is given by the equation 20 + 0.2x, where x represents the number of units produced. The daily revenue per unit is $70. The maximum daily profit occurs when the revenue per unit is equal to the cost per unit. Therefore, we can set the equation:

20 + 0.2x = 70

Solving for x, we get:

x = (70 - 20) / 0.2 = 250

So the maximum daily profit is based on producing 250 units. To calculate the maximum daily profit, we can substitute x = 250 into the cost equation and subtract from the revenue:

Profit = Revenue - Cost

Profit = 70 * 250 - (20 + 0.2 * 250)

Profit = 17,500 - 70 = 17,430

Therefore, the maximum daily profit the Ace Company can expect is $17,430.

User Jmaglio
by
4.9k points
4 votes

Answer:

$3125

Step-by-step explanation:

Cost = x(20 + 0.2x)

= 20x + 0.2x²

MC = 20 + 0.4x

MR = MC

70 = 20 + 0.4x

x = 125

Cost = 20 + 0.2x = 45

Profit per unit = 70 - 45 = 25

Total profit = 125×25 = $3125

User ThatsIT
by
5.7k points