On September 25, 2018 Colson Corp. sold 200,000 widgetrons to Cavanaugh Corp at $5 per unit. Half of the units were delivered on
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Answer:
p1 = $259.53 p2 = $381.20
Explanation:
1. Find the revenue function.
This is a typical income maximization problem. Therefore, the first thing we should know is what are the revenues for each product.
Recall that the revenue is given by P * Q
1.a Find the revenue of the Ultra Mini (product 1):
1.b Find the revenue of the Big Stack (product 2):
2. Find the marginal revenues.
The revenue function must be derived from the price.
For product 1, we derive from P1:
For product 2, we derive from P2:
3. Create a system of linear equations in two unknowns
With the marginal revenue functions we create a system of linear equations in two unknowns (p1 and p2) and equal 0.
4. Resolve the previous system
4.a. To make it easier, we can rethink the terms of the system like this:
is the same as saying:
And is the same as saying:
Therefore:
Notice that now we only have one unknown (P1).
4.b. In order to eliminate fractionals, we can multiply both terms by 400:
4.c. We solve the equation, putting numbers on one side and unknowns on the other:
4.d. Once P1 has been identified, we replace it in any of the terms of the original system of equations (those established in 4.a).