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1. The saw near me on River Road can convert logs into lumber and plywood at the rate of 400 units per week. 100 units of lumber and 150 units of plywood are already pre-sold to Home Depot. Profit is $20/unit for the lumber and $$30/unit for plywood. How many units of each should be produced to maximize their profit (Maximizing Problem).
2. Nutrition is always an issue in the United States. Suppose it takes 12 units of carbohydrates and 6 units of protein to satisfy my weekly nutrition requirement. Boiled ham contains 2 units of carbohydrates and 2 units of protein per pound, and costs $3.50/lb. Cheese contains 3 units of carbohydrates and 1 unit of protein per poundand costs$4.60/lb. How many pounds of each are needed to minimize costs and still meet the minimum nutrition requirement? (Minimizing Problem).
3. Solve the following:
x - 5y = 4
y = 7 - 2x
4. Solve the following:
x + 2y = 2
4x + 4y = 5
Description of Probabilities, A survey of MBA students obtained the following data on "student's first reason for application to the school in which they matriculated".
estimate the probability that in a group of 500 randomly selected drivers, at least 40% had accidents in the last year. Based on that result, is there strong evidence supporting the claim that the accident rate in New York City is higher than 34%?
Write a Matlab script to do the following. Assign m and n to 3 and 4 respectively, create a m by in matrix with terms a_ij=i*j and call t A and then multiply A by random 4x4 matrix
Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once thr..
Assuming that the position function is continuous and differential during this 5 minutes interval, prove that the car broke the 55mph speed limit somewhere between points A and B.
The demand equation for a product is p = 45 - .01q. Write the revenue as a function of q and find the quantity that maximizes revenue. What price corresponds to this quantity? What is the total revenue at this price?
Different ways to schedule appearances of 4 performers. There are 4 performers who will present their comedy this weekend at a comedy club
What is the line of symmetry? Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h)2 + k.
Four years after paying $2300 for shares in a startup company, you sell the shares for $2100(at a loss). What is the total return in percentage and the annual return in percentage?
According to the data from the U.S. Department of Commerce, movie-theater box-office receipts (in millions of dollars) in year x can be approximated by y= 535.43x+5362.21, where x=0 corresponds to 1995. Assume that this equation remains valid unti..
Use Lagrange multipliers to show that the shortest line segment connecting P to the sphere is that which extends through the center of the sphere.
The strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from a circular cylindrical log of radius r.
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