We have 3,000 Units of product to sell over a five day period. From historical s

Question

We have 3,000 Units of product to sell over a five day period. From historical sales data, we have estimated the following demand curves P=price/unit in $ Q=number of units sold Day 1: P=10-0.01Q valid for prices between $3and $8. Day 2: same as Day 1 Day 3: P= 15-0.01Q valid for prices between $6 and $10 Day 4 P=20-0.01Q valid for prices between $6 and $12 Day5: same as Day 1 The revenue maximizing price for Day 1 is (Hint: Please keep one decimal point.), and quantity sold is (Hint: Please enter an integer.). The revenue maximizing price for Day 2 is (Hint: Please keep one decimal point.), and quantity sold is (Hint: Please enter an integer.). The revenue maximizing price for Day 3 is (Hint: Please keep one decimal point.), and quantity sold is (Hint: Please enter an integer.). The revenue maximizing price for Day 4 is (Hint: Please keep one decimal point.), and quantity sold is (Hint: Please enter an integer.). The revenue maximizing price for Day 5 is (Hint: Please keep one decimal point.), and quantity sold is (Hint: Please enter an integer.). The current answer posted on chegg.com is not correct. I am supposed to use excel solver for this, but i'll take anything at this point.

Explanation / Answer

The maximum revenue can be earned on day four as maximum price for the product is allowed For Day 4 P=20-0.01Q

so R = P*Q = 20Q-0.01Q^2 and MR=dR/dQ = 20-0.02Q Now for MR to be maximum MR=0

Q = 20/0.02=1000 and P = 20-0.01*1000 = 10

The next maximum revenue can be earned on day three as next high price for the product is allowed For Day 3 P=15-0.01Q

so R = P*Q = 15Q-0.01Q^2 and MR=dR/dQ = 15-0.02Q Now for MR to be maximum MR=0

Q = 15/0.02=750 and P = 15-0.01*750 = 7.5

Q remaining remining for day 1,2 and 5 is 1250

The revenue can be earned on any of these days P=10-0.01Q

so Q=1250/3 = 416.7 per day an day 1,2,5

P = 10-0.01*1250/3 = 5.8

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