A company sells two types of candies: CanDy4 and CanDyBy. The selling price of a

Question

A company sells two types of candies: CanDy4 and CanDyBy. The selling price of a unit of CanDy4 is p1 dollars and there are 60 + p1 + p2 number of CanDy4 units sold by the company. The selling price of a unit of CanDyBy is p2 dollars and there are 80 + p2 + p1 number of CanDyBy units sold. It costs $15 to produce a unit of CanDy4 and $22 to produce a unit of CanDyBy. No more than a total of 1; 000 units of CanDy4 and CanDyBy can be produced. It is also noted that the total cost of producing CanDy4 and CanDyBy cannot exceed 9; 300$. Formulate and solve (by using Matlab) a nonlinear programming problem (NLP) that will determine the maximum proÖt of selling two candies.

Explanation / Answer

d. Nash equilibrium occurs at where two reaction curve intersect. That is

[p2=90+rac{1}{4}*(90+rac{p2}{4})]

[p2=120]

Substituting p2=120 into company 1's recation function we have

[p1=90+rac{120}{4}]

[p1=120]

Nash equilibrium prices p1=120 and p2=120

e. If company 1 chooses its price p1 then accoeding to reaction function company 2 will choose price as

p2=90+p1/4.

Now company will choose that price which maximizes its revenue considering company2's reaction function intto its revenue function. That is

[MaxR1=1000(90p1-0.5p1^{2}+0.25p1(90+rac{p1}{4}))]

[MaxR1=1000(90p1-0.5p1^{2}+22.5p1+0.0625p1^{2})]

First order condition gies us

[90000-p1+22.5+0.125p1=0]

[or, p1=rac{720180}{7}]

Then company 2 will choose price

[p2=90+rac{720180}{7*4}=rac{180675}{7}]

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