Show the problem formulation with variables identified, objective

function and constraints listed in the form of equations $($like the class

examples$).20$ points.

$-$ Show the completed excel model for the linear programing $($like the

class examples$)10$ points.

$-$ Show the complete linear programming answer report generated from

excel solver, showing the output of the objective function, variables

and constraints $($like the class examples$)10$ points.

Question $1-$ Maximization problem $-$

A tire manufacturer produces two sizes of tire for a popular car in the

market. The car company has agreed to buy the tires for next $12$ months.

The tire manufacturer now has tasked their operations manager to

identify the number of tires to produce for each size to achieve

maximum revenue. When sold to the car company, tire R$17$ sells for $25$

dollars a piece and tire R$19$ sells for $32$ dollars a piece.

The tire manufacturer has a labor hours capacity of $15,000$ hours and

budget for raw material limited to $ $1,150,000.$

Tire R$17$ utilizes $0\mathrm{.}2$ hours of labor and $$15$ of material cost per piece

whereas, tire R$19$ utilizes $0\mathrm{.}25$ hours of labor and $$20$ of material cost

per piece.

Formulate a LP model and solve in excel solver to calculate the optimal

quantities of each type leading to maximizing the revenue and satisfying

all constraints.