Answer:
b(x) = (3+0.5x) (38-4x)
Step-by-step explanation:
Let the generated revenue per day be b(x)
Let x be the number for every 50cents($0.5) price increase
Formula to be used to generate the revenue generated is expressed using the formula:
b(x) = Price × Quantity
Next is to derive the price and quantity function in terms of x.
For the price:
If he currently charges $3 per book
Let derive the price function for the model and x number of price increase for every 50 cents, then
Price = ($0.5 of x)+$3
Price = $3+$0.5x
Price = $(3+0.5x)
For the quantity:
Number of books rent out per day = 38
If for every 50cents increase in rental price x, the average business can expect to lose 4 rentals a day, then the total lost per quantity = 4x
Quantity per time = Number of books rent out daily - loss on each book
Quantity = $(38-4x)
Next is to substitute the price and quantity function into the revenue formula above:
Revenue = Price × Quantity
Revenue = (3+0.5x)(38-4x)
Hence the equation that models this scenario, where b(x) is the revenue generated and x is the number of 50 price increases is b(x) = (3+0.5x)(38-4x)
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