The demand equation for your company\'s virtual reality video headsets is p = 1,

Question

The demand equation for your company's virtual reality video headsets is p = 1,500 q0.3 where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $110 per headset. (a) What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ How many headsets will your company sell at this level of profit? (Give your answer to the nearest whole number.) q = headsets (b) How much, to the nearest $1, should your company charge per headset for the maximum profit? p = $

Explanation / Answer

Profit = Revenue - Cost
Revenue = price x quantity sold = pq = [1500/q^0.3] q
Revenue = 1500 q^0.7
Cost = 110q

Profit = 1500q^0.7 -110q
differentiate the profit with respect to q
dP/dq = 1500 (.7) q^(.7-1) - 110
1050/q^0.3 - 110 = 0
1050 - 110q^0.3 = 0
110q^0.3 = 1050
q^0.3 = 1050/110
q = 1845

Substitute this q into the profit
Profit = 1500q^0.7 -110q
Profit = 289908 - 202950
Profit = 86958
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q= 1845 headsets
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p = 1500/q^0.3 = 1500/(1845)^0.3 = 157.14

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