Question

Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? explain why this is true.

Answer 1

The desired minimum revenue is $130.

What is revenue?

Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.

• The money received from routine business activities is referred to as revenue, sales, or the top line.

• Revenue (from the sale of goods or services) less operational expenses equals operating income.

• Non-operating income is irregular or irregular money that comes from other sources (e.g., lawsuit proceeds).

• Governments, nonprofit organizations, and private persons are examples of non-business entities that also declare revenue, albeit their methods and resources vary.

Let us assume,

charge = b

customer= c

revenue= r

We know that,

r= bc

⇒ $r=16\times 10$

⇒ $r=\ 160$

Also,

$b+1$ ⇒ $c-2$

with a target of $r \geq 130$

Therefore,

$b=10+x$ ⇒ $c=16-2x$

$(10+x)(16-2x)\geq 130\\160-20x+16x-2x^2 \geq 130\\-2x^2 -4x+30\geq 0\\x^2+2x-15\leq 0\\(x+1)^2 \leq 4^2\\x+1 \leq 4$

as negative value is not considered.

$x\leq 3$

We get the result that 3 is the maximum increase amount.

Therefore, revenue will be:

$(10+3)(16-3\times2)=13\times 10$

revenue = 130

Full Question: Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.

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