You are using a sturdy building material to design a water fountain basin for a park in the city. The bottom and sides of the ba
sin should be 1 foot thick. Its outer length should be twice its outer width an outer height. Let x represent the outer height and outer width.
1. Use the interior length, interior width, interior height, and the volume to write a polynomial equation that represents the situation.
2. Write the polynomial equation in standard form.
3. Factor the polynomial equation and solve for x.
4. Determine the lengths of the basin.
1. Use the interior length, interior width, interior height, and the volume to write a polynomial equation that represents the situation.
2. Write the polynomial equation in standard form.
3. Factor the polynomial equation and solve for x.
4. Determine the lengths of the basin.
1 answer:
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Answer:
a) Demand function:
b) The rebate should be of $200, so the sale price becomes $300 per unit.
c) The rebate should be of $150, so the sale price becomes $350 per unit.
Step-by-step explanation:
a) In this case, we have a known point of the demand function (1000 units sold at $500), and the slope of a linear function (increase by 100 units fora decrease in $10).
We can express the demand function (linear) as:
To calculate the slope m, we use:
To calculate b, we use the known point and the calculated slope:
Then the demand function is:
b) The revenue can be expressed as:
To maximize, we can derive and equal to zero
The rebate should be of $200, so the sale price becomes $300 per unit.
c) If we take into account the cost, we have that
To maximize, we can derive and equal to zero
The rebate should be of $150, so the sale price becomes $350 per unit.