Consider a capital budgeting example with 5 projects from which to select.

Consider a capital budgeting example with 5 projects from which to select. Let x1 = 1 if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75, and $300 respectively. The budget is $450. Write the appropriate constraint for the following conditions: Choose no fewer than 3 projects. If project 3 is chosen, project 4 must be chosen. If project 1 is chosen, project 5 must not be chosen. Write the appropriate constraints for the budget constraint. No more than 2 of projects 1, 2, and 3 can be chosen.

Lagrange

Please see attachment.

Newton's interpolating polynomial

see attachment Use Newton’s interpolating polynomial to approximate the function: f (x) = e^ (–ax2) a = 1.1125 Construct approximation using the values f (x) at x= -2, -1, 0, 1, 2. Call this approximation N(x). ii) Compute the value of the integral accurate to 1 decimal place. iii) Compute sufficient trapezium rule and the mid-point rule estimates for the integral So that you may quote the integral’s value to 1 decimal place. Hence compute the corresponding Simpson’s rule estimate. Is N(x) a good approximation to f(x)? Give a reason.

Lagrange

Please see attachment Compute the Lagrange interpolating polynomial L(x) for the function f(x) f (x) = √(cos(ax)) a = 1.1125 passing through the points (0, f(0)), (0.5, f(0.5)) and (1, f(1)). Let S1 be the first Simpson’ rule approximation to Show that

Linear Programming

The lakeside boatwork is planning to manufacture three types of molded fiberglass recreation boats, a fishing (bass0 boat, a ski boat, and a small speedboat. The estimated selling price and variable cost for each type of boat are summarized in the following table Bass $12,500 $23,000 Ski 8,5000 18,000 speed 13,7000 26,000 The company has incurred fixed costs of 2,800.000 to set up its manufacturing operation and begin production.Lakeside has also entered into agreements with several boat dealers in the region to provide a minimum of 70 bass boat, 50ski boats and 50 speedboats. Alternatively the company is unsure of what actual deman will be so it has decided to limi... click for more