MCV4U1 – UNIT THREE Lesson Four LESSON 4: OPTIMIZATION PROBLEMS CONTINUED 1. A tool manufacturing company determines that when the level of production is x units, the cost of production, in dollars, is modeled by the equation C x 0.05 x 9 x 300, 0 x 3000 . What level C x of production will minimize the unit cost, which is given by U x ? x 2. A can for vegetables is to have volume 350 cm 3 . The material for the top and bottom costs $0.50 / cm 2 while the material for the sides costs $0.30 / cm 2 . Determine the dimensions of the can that minimize the cost of materials. 3. A store has been selling 200 DVD players a week at $350 each. A market survey indicates that for each $10 decrease in price, the number of DVD players sold will increase by 20 per week. What should the DVD price be to maximize profit?