Finite Mathematics: Suppose that Tesla has dealerships in Fresno and Walnut Creek and manufacturing facilities in Menlo Park and Fremont. The cost of shipping each Tesla car from Menlo Park to Fresno is $20; from Menlo Park to Walnut Creek, $30; from Fremont to Fresno, $20; and from Fremont to Walnut Creek, $25. Suppose that the Menlo Park factory has a stock of 400 Teslas, whereas the Fremont factory has a stock of 250. The Fresno dealership orders 250 cars and Walnut Creek orders 200. Tesla wants to ship the cars for these orders in such a way that the cost is minimized. (a) Create a transportation diagram where arrows are labeled with the corresponding decision variables. (b) What is the objective? (c) Give all constraints for this linear programming problem. (d) Complete the following table (some values may be left blank). Constraint Inequality Slope-Intercept Form x-intercept y-intercept (e) Use the table from part (d) to graph the feasible set. (f) In the graph from part (d), label the vertices of the feasible set. Determine the coordinates of the vertices (show work where necessary). (g) Using the Fundamental Theorem of Linear Programming, determine the optimal shipping schedule. What is the minimum cost?
Finite Mathematics:
Suppose that Tesla has dealerships in Fresno and Walnut Creek and manufacturing facilities in Menlo Park and Fremont. The cost of shipping each Tesla car from Menlo Park to Fresno is $20; from Menlo Park to Walnut Creek, $30; from Fremont to Fresno, $20; and from Fremont to Walnut Creek, $25. Suppose that the Menlo Park factory has a stock of 400 Teslas, whereas the Fremont factory has a stock of 250. The Fresno dealership orders 250 cars and Walnut Creek orders 200. Tesla wants to ship the cars for these orders in such a way that the cost is minimized.
(a) Create a transportation diagram where arrows are labeled with the corresponding decision variables.
(b) What is the objective?
(c) Give all constraints for this linear programming problem.
(d) Complete the following table (some values may be left blank).
Constraint Inequality Slope-Intercept Form x-intercept y-intercept
(e) Use the table from part (d) to graph the feasible set.
(f) In the graph from part (d), label the vertices of the feasible set. Determine the coordinates of the vertices (show work where necessary).
(g) Using the Fundamental Theorem of Linear Programming, determine the optimal shipping schedule. What is the minimum cost?
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 1 images
