In a Paper Business Two Types of Paper Are Being $\$ 5.00$

In a paper business two types of paper are being made-sponge and cloth. Sponge sells for $\$ 5.00$ per package, and cloth sells for $\$ 3.00$ per package. Let $X_{1}$ be the number of packages of sponge sold and $\mathrm{X}_{2}$ the number of packages of cloth sold. Direct costs are $\$ 0.25$ times the square of the number of units of sponge sold and $\$ 0.05$ times the square of the number of units of cloth sold. Fixed costs for the two paper types together are $\$ 10.00$ for all the volumes contemplated or possible. There are no other costs or revenues. However, all paper rolls have to be labeled by a single labeling machine which can handle at most 50 rolls of both types put together. Find the net profit maximizing combination of sponge and cloth to be sold subject to the constraint. (It may be assumed that the firm can sell whatever volume they produce.)