The American Safety Council has allocated $500,000 for projects designed to prevent automobile accidents. Four proposals were submitted: (a) TV advertisements, (b) teenage safety education, (c) improved airbags, and (d) enforcement of driving laws. The projects are expected to result in the reduction of both fatalities and property damage, as shown in the table to the right. The council has decided that no single project will be awarded more than $250,000. They also wish to award at least $50,000 for teenage education. Finally, they want to award at least $1 for improved airbags for each dollar awarded for TV advertisements. The federal government, for internal analysis purposes, has as- sessed the average value of a human life as being $400,000. Expected Reduction in Fatalities per $1,000 0.25 0.32 0.15 0.28 Average property damage averted per $1,000 300 500 Project A TV Advert B Teenage educatio Airbags C D Laws 250 500000 Budget Life Value 400000 250000 50000 Max award Project B Min Formulate the initial Tableau for the Simplex Method

Solve the problem.The following is known about three numbers: If the second number is subtracted from the sum of the first number and 3 times the third number, the result is -7. The third number plus 2 times the first number is -2. The first number plus 5 times the second number plus the third number is 3. Find the three numbers.[Hint: let x represent the first number, y the second number, and z the third number. Use the given conditions to write and solve a system of equations.]

A tortoise challenged a hare to a 100-meter race on a track. The tortoise negotiated a 50-meter head start with the hare. When the race started the hare was running at a constant speed of 2.8 meters per second and the tortoise was crawling at a speed of 0.5 meters per second. (They both maintained these speeds for the entire race.)   Our goal is to determine who won the race. Read the above problem statement again, then explain in writing on a sheet of paper how you will determine who won the race. Construct a drawing to represent the 100-meter length of the track. Then place the tortoise and hare's starting points on the track. Define the variable t to represent the number of seconds since the start of the race. Write an expression to represent the Tortoise's distance from the starting line in terms of t.    Represent the Hare's distance from the starting line in terms of t.      Write a formula to represent the distance, d (in meters), that the tortoise is ahead of the hare in…

please answer part d as well. i dont see the solution anywhere here.