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AysviL [449]
3 years ago
15

A company has established that the relationship between the sales price for one of its products and the quantity sold per month

is approximately p equals 70 minus 0.1 Upper Dp=70−0.1D ​(D is the demand or quantity sold per month and p is the price in​ dollars). The fixed cost is ​$1 comma 5001,500 per month and the variable cost is ​$3535 per unit produced. a. What is the maximum profit per month for this​ product?
Business
1 answer:
Vilka [71]3 years ago
8 0

Answer:

max profit at MR = MC  is 1,562.5 dollars

Explanation:

we need to solve for the point at which MR = MC

First we calculate marginal revenue, the revenue generate from an additional units which, is the slope of the revenue function

p = 70 - 0.1Q

total revenue = (70 - 0.1Q)Q = -0.1Q^2 + 70Q

dR/dq= -0.2q + 70

Then we do the same for marginal cost, the cost to produce another unit:

total cost: 1,500 + 35 Q

dC/dq = 35

Now we equalize and solve:

-0.2q + 70 = 35

70 - 35=0.2q

35/0.2 = q = 175

p = 70 - 0.1 (175) = 70 - 17.5 = 52.5

52.5Q - 1,500 - 35Q = profit

52.5 x 175 - 1500 - 35 x 175 = profit

profit = 1562.5

if we calcualte for one up or down:

Q = 174 then profit = 1562.4

Q = 176 then profit = 1562.4

This profit is lower than our maximize point, so we agree this is the max point.

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Complete Question:

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B. relative market share, the ability to match or beat rivals on key product attributes, brand image and reputation, costs relative to competitors, and the ability to benefit from strategic fits with sister businesses.

Explanation:

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1. Relative market share: this measures the subsidiaries position in a market in relation to its competitors in the same industry. It is a measure of the percentage of the market they control.

2. The ability to match or beat rivals on key product attributes: this is really important in the assessment of competitive strengths because it represents the level of acceptance of their products by consumers in comparison with rivals.

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