$12\mathrm{.}3-4.$ The Toys$-$R$-4-$U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $$50,000$ for toy I and $$80,000$ for toy $2.$ Once these costs are covered, the toys would generate a unit profit of $$10$ for toy $1$ and $$15$ for toy $2.$ The company has two factories that are capable of producing these toys. However, to avoid doubling the start$-$up costs just one factory would be used, where the choice would be based on max$-$ imizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy $1$ can be produced at the rate of $50$ per hour in factory $1$ and $40$ per hour in factory $2.$ Toy $2$ can be produced at the rate of $40$ per hour in factory $1$ and $25$ per hour in factory $2.$ Factories $1$ and $2,$ respectively, have $500$ hours and $700$ hours of production time available before Christmas that could be used to produce these toys. It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many