A business is currently selling 30 chairs per day for a price of $25 p

Question

A business is currently selling 30 chairs per day for a price of $25 per chair. A worker predicts that if the business chooses to lower the cost of the chairs, then for every $1 the price is lowered, one more chair will be sold. If the prediction is accurate, what is the maximum revenue the business can earn in a day from selling chairs? (Revenue is the amount of money that the business takes in, without consideration of expenses or other costs.)

A. $600
B. $650
C. $700
D. $750
E. $800

A. $600
B. $650
C. $700
D. $750
E. $800

ShahadatHJ · Answer

Current Situation: chairs per day 30 and $25 per chair.

Hence, revenue: 30*25=$750

Now consider the given prediction. Let's say, per chair ($25 to $24) and total chairs (30 to 31)

Revenue becomes: 31*24=$744

We can see the revenue decreases. If you go with more chairs and a lesser price per chair the sales revenues keep going down.

So, the maximum can they earn is by selling 30 chairs at $25.

Ans: $750

stne · Answer

Alternate soln.

Price per chair  \frac{25}{30}=.83

So we are reducing $1 and for one extra chair we are adding  $.83

So increase in revenue is not able to compensate for the decrease in price .

If we reduce the price by  $2  then increase for two extra chairs will be  $ .83*2= $1.66

For  $10  reduction we would sell  10  extra chairs or get .83*10 = $8.3   extra revenue.

So we can see that we would always be reducing more than we would be adding.

Hence workers prediction is false.

Hence current price is the best price.

Ans- D

hope it's clear.

ScottTargetTestPrep · Answer

Solution:

Let x be the number of dollars the price of a chair is lowered from $25 (notice that x is also the number of more chairs that can be sold beyond 30). Since revenue = quantity * unit price and if we let y be the revenue, we have:

y = (30 + x)(25 - x)

y = 750 - 5x - x^2

y = -x^2 - 5x + 750

Notice the equation above is a quadratic equation whose graph is a downward parabola. So the maximum revenue is the y-coordinate of the vertex. For a quadratic equation of the form y = ax^2 + bx + c (where a ≠ 0), the maximum value occurs when x = -b/(2a). Since here, a = -1 and b = -5, the maximum value occurs when x = -(-5)/(2 * -1) = -2.5. Since x is negative and we only concern ourselves with the values of y where x is nonnegative, it means the maximum value of y occurs at x = 0. Therefore, the maximum revenue is y = (30 + 0)(25 - 0) = 30 * 25 = $750. (In other words, do not lower the price. For example, if you lower the price by $1 to $24, the number of chairs sold increases by 1 to 31. However, the revenue will then be 31 x 24 = $744, which is lower than $750.)

Answer: D

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A business is currently selling 30 chairs per day for a price of $25 p

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