Two models of a product - Regular (X) and Deluxe (Y) - are produced by a company. A linear programming model is used to determine the production schedule. The formulation is as follows:

Maximize profit = 50X + 60Y

Subject to:

8X + 10Y=800 (labor hours)

X + Y=120 (total units demanded)

4X + 5Y =500 (raw materials)

all variables =0

The optimal solution is X = 100, Y = 0

How many units of the regular model would be produced based on this solution?

A. 0
B. 50
C. 100
D. 120

What is the equation of the line in point-slope form? y+ 4 = 1/2(x+4) y-4 = 1/2(x + 4) y-0 = 2(x - 4) y-4 = 2(8-0)

The sum of these consecutive integers is equal to 9 less than 4 times the least of the integer. find the three integers

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?