Question $1$ options:

The demand function for potato chips is Q$=21-$P$,$ where Q is ounces and P is the price $($in cents$)$ per ounce. Assume that it costs you $2$ cents per ounce to produce potato chips.

Set up your spreadsheet properly so that you can conduct nonlinear pricing. See the Chapter $6$ lecture slides or Chapter $6$ of the book. Your spreadsheet should be setup to the point where you are ready to run evolutionary solver to conduct nonlinear pricing.

This involves packaging the potato chips in a small package and a large package. You will charge different average price per ounce for the two packages.

Note that this problem will be very similar to the power company problem we did during lecture. You need to optimize your profit over three variables $-$ the cutoff $($CUT$),$ the high price $($HP$),$ and the low price $($LP$).$ Note that CUT will be the size of the small package and HP will be the price per$-$ounce of the small package. The size of the large package will equal the number of Units Bought. The LP is the price of all units that exceed CUT. The average price per ounce of the large package isn't simply LP$.$ It is

where UB is "Units Bought."

This is because the average price of the large package will consist of the weighted average of HP price up to CUT and the LP price for all ounces greater than CUT up to the number of units bought. So for example, if a small package is $4$ ounces and a large package is $10$ ounces, then CUT$=4.$ If HP$=25(25$ cents per ounce$),$ then the average price for the $4$ ounce small package is $25.$ If LP$=15,$ then the average price for the large package is

$.$

You will now be asked a series of questions.

$($Note: You must enter a number very precisely. Insert a number up to two decimal places. If Excel reports a number greater than two decimal places, round the number so it has only two decimal places. If you have a number like $"10\mathrm{.}5"$ then you must enter $10\mathrm{.}50$ not just $10\mathrm{.}5.$ If you have a whole number like $"10",$ then you must enter $10\mathrm{.}00).$

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2($Just plug these values into the spreadsheet and do not run Solver$),$ what is the WTP at Unit$=13?$

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is the "Gross Value" at Unit$=12?$

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is the "Amount paid" at Unit$=18?$

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is the "Consumer Surplus" at Unit$=16?$

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is the number of Units bought?

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is your Revenue?

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is the Production cost?

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2,$ what is your Profit?

If you ran Evolutionary Solver with starting values of CUT$=5,$ HP$=5,$ and LP$=5$ with no constraints does the realized profit come within $1\%$ of the maximum profit of $$181\mathrm{.}00($you should run solver at least twice$)?$

$($Note: Answer "yes" or $"$no$").$

Now add the constraints that CUT$>=1,$ CUT$<=20,$ CUT must be an integer, and LP and HP are between $0$ and $40.$ If you ran Evolutionary Solver with the same starting values of CUT$=5,$ HP$=5,$ and LP$=5$ does the realized profit come within $1\%$ of the maximum profit of $$181\mathrm{.}00($you should run solver at least twice$)?$

$($Note: Answer "yes" or $"$no$").$

Now add the constraints that CUT$>=1,$ CUT$<=20,$ CUT must be an integer, and LP and HP are between $0$ and $15.$ If you ran Evolutionary Solver with the same starting values of CUT$=5,$ HP$=5,$ and LP$=5$ does the realized profit come within $1\%$ of the maximum profit of $$181\mathrm{.}00($you should run solver at least twice$)?$

$($Note: Answer "yes" or $"$no$").$

Now go back to the starting values of CUT$=9,$ HP$=19,$ and LP$=2($Just plug these values into the spreadsheet and do not run Solver$).$ What is the size of the large package?

Using the starting values of CUT$=9,$ HP$=19,$ and LP$=2.$ What is the average price of the small package?

Now go back to the starting values of CUT$=9,$ HP$=19,$ and LP$=2.$ What is the average price of the large package?