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. By how much would the profit contribution of product A has to increase before it will be profitable to produce A$?$ $$1$E$+30$ $$0$ $$10$ $$20$ $$132\mathrm{.}5$