In andrew’s furniture shop, he builds bookshelves and tables. each type of furniture takes him about the same time to make. he figures he has time to make, at most, 25 pieces of furniture by this saturday. the materials for each bookshelf cost him $20.00 and the materials for each table cost him $45.00. he has $675.00 to spend on materials. andrew makes a profit of $60.00 on each bookshelf and a profit of $100.00 for each table. how many of each piece of furniture should andrew make to maximize profit? a. define variables b. write the constraint inequalities that represent the situation, and explain what each of the inequalities represents. (you should have four inequalities.) c. what are the vertices of the feasible region?

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?