Use this information, along with its associated Sensitivity Report, to answer the following questions.

A production manager wants to determine how many units of each product to produce weekly to maximize weekly profits. Production requirements for the products are shown in the following table.

Material $1$ costs $$7$ a pound, material $2$ costs $$5$ a pound, and labor costs $$15$ per hour. Product A sells for $$101$ a unit, product B sells for $$67$ a unit, and product C sells for $$97\mathrm{.}50$ a unit. Each week there are $300$ pounds of material $1$; $400$ pounds of material $2$; and $200$ hours of labor. The output of product A should not be more than one$-$half of the total number of units produced. Moreover, there is a standing order of $10$ units of product C each week.

What is the optimal objective function value?

$925$

none of these

$100$

$825$

$92\mathrm{.}5$