Peter Piper, an enterprising entrepreneur, has decided to expand his small business. He has added his own Peters Picante Pepper Sauce to his product line which includes the popular Peters Picked Pepper Pickles.However, since its launch a month ago, Peters Picante Pepper Sauce has not done as well as Peter had expected.Prior to launch, Peter had done his own market survey that indicated very strong demand from the pepper loving inhabitants the town of West$-$Ham$-$End$-$River$-$Estate $($WHERE$),$ some even suggested they would pay premium prices for Picante Pepper Sauce.Peter believes he can improve revenues and profitability if he could get a reliable estimate of demand for the Picante Pepper Sauce. He hired an economist who conducted three $(3)$ separate exercises to estimate demand for the sauce. As a conservative businessman with little appetitive for risks, Peter has insisted that he would only accept estimates that are reliable with a confidence of $99\%$ and above.The relevant information for the demand estimates are shown below:$($T values are shown in brackets below the parameter estimates$)$Function $1($estimated using data from $16$ observations$)$ Q$=4005\mathrm{.}5$P$+0\mathrm{.}9$A$-2$P$*+0\mathrm{.}8$Y $($R$2=0\mathrm{.}96)(4\mathrm{.}0)(2\mathrm{.}91)(3\mathrm{.}0)(2\mathrm{.}0)(2\mathrm{.}85)$Function $2($estimated using data from $21$ observations$)$ Q$=4004\mathrm{.}0$P$+0\mathrm{.}9$A$+0\mathrm{.}8$P$*+0\mathrm{.}8$Y $($R$2=0\mathrm{.}95)(4\mathrm{.}0)(2\mathrm{.}83)(2\mathrm{.}9)(2\mathrm{.}78)(2\mathrm{.}85)$Function $3($estimated using data from $31$ observations$)$Q$=4003\mathrm{.}5$P$+0\mathrm{.}9$A$+0\mathrm{.}9$P$*+0\mathrm{.}8$Y $($R$2=0\mathrm{.}95)(4\mathrm{.}0)(2\mathrm{.}76)(2\mathrm{.}80)(2\mathrm{.}75)(2\mathrm{.}85)$UNIVERSITY OF GUYANADEPARTMENT OF ECONOMICSWhere:Q is daily sales,P is the price of Peters Picante Pepper Sauce,A is daily advertising cost,P$*$ is the price of Peters Picked Pepper Pickles, andY is the per$-$capita daily disposable income for residents of WHERETo$-$date, Peter has been charging a fixed price of $$5$ for Picked Pepper Pickles and an introductory price of $$2\mathrm{.}5$ for Picante Pepper Sauce. The cost of producing one bottle of sauce is $$2$ and Peters daily advertising budget for the sauce is fixed at $$200.$ The Bureau of Statistics for WHERE has reported stable daily per$-$capita disposable income of $$300.$If Peter decided to provide the competitive level of sauce to the market, how many bottles per day would he provide and at what price? What would be his profit at this level of sales?