Transatlantic air travel in business class has an estimated elasticity of demand of 0.62, while transatlantic air travel in economy class has an estimated price elasticity of 0.12.

Aquatic marine stores company manufactures special metallic materials and decorative fittings for luxury yachts that require highly skilled labor. aquatic uses standard costs to prepare its flexible budget. for the first quarter of the year, direct materials and direct labor standards for one of their popular products were as follows: direct materials: 3 pounds per unit; $ 6 per pound direct labor: 4 hours per unit; $ 19 per hour during the first quarter, aquatic produced 5 comma 000 units of this product. actual direct materials and direct labor costs were $ 65 comma 000 and $ 330 comma 000, respectively. for the purpose of preparing the flexible budget, calculate the total standard direct materials cost at a production volume of 5 comma 000 units.

You are thinking of making your mansion more energy efficient by replacing some of the light bulbs with compact fluorescent bulbs, and insulating part or all of your exterior walls. each compact fluorescent light bulb costs $4 and saves you an average of $2 per year in energy costs, and each square foot of wall insulation costs $1 and saves you an average of $0.20 per year in energy costs.† your mansion has 150 light fittings and 3000 sq ft of uninsulated exterior wall. to impress your friends, you would like to spend as much as possible, but save no more than $750 per year in energy costs (you are proud of your large utility bills). how many compact fluorescent light bulbs and how many square feet of insulation should you purchase? how much will you save in energy costs per year? (if an answer does not exist, enter dne.)

Describe three scenarios in which you might utilize mathematics to investigate a crime scene, accident scene, or to make decisions involving police practice. be sure to explain how math is used in police as they work through each scenario.