Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100
ID: 3107483 • Letter: A
Question
Annual profit in thousands of dollars is given by the function, P(x) = 12x - 100, where x is the number of items sold in thousands, x 10.
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P(x)=12x-100
The meaning of 12 is:
It is profit associated with every product sold.
The meaning of -100 is:
It is the amount of fixed cost.
Explanation:
Total revenue R(x)=Price of product X no. of product sold=zx
Total cost C(x)= (Variable cost per product X no. of product)+ Fixed cost=ax+100
Assume that all products have been sold.
P(x)=zx-{ax+100}=(z-a)x-100=12x-100
This is profit.
3.
x
Profit
8
-4
10
20
13
56
16
92
21
152
x
Profit
8
-4
10
20
13
56
16
92
21
152
Explanation / Answer
5. The profit function as stated has no maximum (in theory). As the graph clearly shows, as more of the product is sold, profit increases at a steady rate, and assuming no other factors, will continue to do so.
6. This profit function can only hold true so long as the business can continue to supply and direct enough of their product as per demand, maintain a steady rate of payroll (with respect to profit) for necessary extra staff as demand may grow, etc.
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