Formulate but do not solve the following exercise as a linear programming problem. A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours. If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P  =             subject to the constraints board feet             labor-hours                     x ≥ 0         y ≥ 0

Problem 4. (Flux) Given the surface M defined by the parametric formula r(u, v) = (u, v, u² + v²) where 0≤u≤ 1,0 ≤ v ≤ 1 and the vector field compute the flux JJM F.dS F = (P, Q, R) = (-z, xy, x) - = [[Pdy ^dz + Qdz ^dz + Rdx / dy M

Discount printers manufactures two types of inkjet printers, a consumer version and a business version. The company can make a total of 119 printers per day, and it has 219 labor hours per day available. It takes 1 labor- hour to make a consumer inkjet printer and 3 labor-hour to make a business inkjet printer. The profits are $35 per consumer inkjet printer and $60 per business inkjet printer. (Use x for consumer inkjet printer and y for business inkjet printer.) Maximize P = 119 <219 subject to Enter the solution to the simplex matrix below. If there is no solution enter 'DNE' in the boxes below. If more than one solution exists, enter only one of the multiple solutions below. If needed, round all answers to the nearest whole. Maximum profit is $ Number of consumer inkjet printer to maximize profit is Number of consumer business printer to maximize profit is

Linear programming model

Bata Aerobics manufactures two models of steppers used for aerobic exercises, x number of luxury models and y number of standard models. Manufacturing each luxury model requires 10 lb of plastic and 10 min of labor. Manufacturing each standard model requires 16 lb of plastic and 8 min of labor. The profit for each luxury model is $50, and the profit for each standard model is $35. If 6000 lb of plastic and 60 labor-hours are available for the production of the steppers per day, how many steppers of each model should Bata produce each day in order to maximize its profit? (x, y)  =                What is the optimal profit?$

Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200, and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. What are the binding constraints of the feasible region of the optimal solution?     Constraint 2 only     Constraint 1 only…