FuelMotion is an oil company that owns two oil processing plants (in Georgia and Arizona) that produce gasoline from crude oil. Their Georgia Plant produces 2 thousand gallons of premium, 1 thousand gallons of medium, and 6 thousand gallons of regular gasoline every day it operates. Their Arizona Plant produces 3 thousand gallons of premium, 4 thousand gallons of medium and 1 thousand gallons of regular gasoline per day of operation. Chevron has placed an order for 110 thousand gallons of premium, 80 thousand gallons of medium, and 90 thousand gallons of regular gasoline and has asked for the order to be filled within 30 days. If it costs FuelMotion $10,000 per day to operate the Georgia Plant and $20,000 per day to operate the Arizona Plant, then determine how it can fill Chevron's order at minimum cost. Note that it may be necessary to produce more gas than demanded, due to the way the plants operate.
a. Formulate a linear programming model (that is, define the variables, and write down the objective function and all constraints mathematically).
b. Create a spreadsheet model for this problem and solve with Excel Solver.
c. What is the optimal solution? What is the optimal value?

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

y - 25 = 2 ( x - 10 ) should be the answer