dune buggy parts off road

By admin, on March 16th, 2010

my second linear programming question which i DESPERATELY NEED HELP WITH?

also due tomorrow, also i dont understand

The Dune Buggy Co. makes two models of off-road vehicles: the Sane Crab and the Surf Mobile. They produce as many as 15 Sand Crabs and 12 Surf Mobiles per week, but two parts have to be specially ordered: an exhaust manifold clamp and a suspension joint. Each Sand Crabb requires 5 manifold clamps and 2 suspension joints. Each Sruf Mobile requres 3 manifold clamps and 6 suspension joints. The maximum number of clamps available is 81 per week and the maximum number of joints available is 78 per week. It takes 20 hours to assemble a Sand Crab and 30 hours to assemble a Surf Mobile. The company has 12 employees who each work a maximum of 37.5 hours per week. The company has a profit margin of $500 for the Sand Crab and $1000 for each Surf Mobile

If x1 and x2 are the numbers of vehicles of both types (SC and SM) to be produced, we have the following problem:
Profit P = 500*x1 + 1000*x2 – to be maximized;
Constraints: 0 ≤ x1 ≤ 15; 0 ≤ x2 ≤ 12; x1, x2 – integers;
5*x1 + 3*x2 ≤ 81 /clamps/;
x1 + 3*x2 ≤ 78 /joints/;
20*x1 + 30*x2 ≤ 12*37.5 /hours/.

This can be solved either manually by graphing the domain and gradient-vector (5, 10) /proportional to (500, 1000)/, or by some linear programming software if You have such installed on Your computer, the optimal solution being:
x1 = 6; x2 = 11; maximum profit = $14 000.

I came home and read the question somewhat late, hope this will come in time and wish You success tomorrow!

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