(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello! I'm having some difficulty getting the objective function out of this question, any help/hints would be appreciated >.<

Company A prepares to launch a new brand of tablet computers. Their strategy is to release the first batch with the initial price of p_1 dollars, then later lower the price to p_2 dollars to capture more customers. Demand curve follows q=700-p, where p is any price (dollars) and q is the number of ppl (in units of 1000 ppl) who are willing to buy it at price p dollars.

Cost is $300/each to manufacture each tablet, in the first production, and $200 in the 2nd run, due to factory improvements.

Devise a price strategy for Company A to maximize their profit.

2. Relevant equations

Note ppl who alrady bought the tablet at the higher price will not buy it agian after the price drop. Ppl who buy during the second run are only those willing ot buy at price p_2 but not at price p_1

Profit=Revenues less cost

R=pq

*predicted profit for p_1=500$, p_2=400$ is $60million

3. The attempt at a solution

So there's two sets tablets being made for p1 and p2 and we want to max the profit, and

profit= R-C

or f(p,q)= pq-q*C

given demand curve q=700-p , cost for 1st run, $300 cost for 2nd run $200

p(700-p)-q(300q_1+200q_2) ??

(p_1+p_2)(700-p) -q(300q_1+200q_2)??

^I think I'm missing something for the objective function :S and I'm not quite sure where the hint (p1,p2)=(500,400) is 60million comes in.....

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# Constrained Optimization using Lagrange multipliers with Commerce applications

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