The Hardgrave Machine Company produces computer components at its plants in Kingston, ON; Prince George, BC; and Sudbury, ON. These plants supply the demand for orders at Hardgrave's two warehouses in Hamilton and Regina. The tables below present the information of: (1) the production cost and capacity for each of the three plants, and the demand at each of the two warehouses Production Plant Kingston Prince George Sudbury Warehouse Hamilton Regina Monthly Supply (units) 15,000 20,000 25,000 Monthly Demand (Units) 35,000 30,000 Production Cost per Unit (S) $50 $55 $45 Transportation costs per unit from each plant to each warehouse are summarized in the following table: To: Hamilton From: Kingston Prince George Sudbury $10 $25 $15 Regina $20 $30 $20 Recent regulations require that no more than 8,000 units are to be shipped from the plant in Kingston to the Warehouse located in Hamilton. Also, at least 30% of the total computer components shipped to the warehouse in Regina are from the plant in Prince George. Formulate algebraically the above problem to help Hardgrave satisfy the demand at the warehouses at the lowest production and transportation costs. Define the decision variables, objective function, and constraints. DO NOT SOLVE.

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This exercise requires the use of technology.Four sectors of the U.S. economy are (1) livestock and livestock products, (2) other agricultural products, (3) forestry and fishery products, and (4) agricultural, forestry, and fishery services. Suppose that in 1977 the input-output table involving these four sectors was as follows (all figures are in millions of dollars).Determine how these four sectors would react to an increase in demand for livestock (Sector 1) of $2,500 million, how they would react to an increase in demand for other agricultural products (Sector 2) of $2,500 million, and so on. (Round your answers to two decimal places. Let the columns of the matrix be given in millions of dollars.)     To 1 2 3 4 From        1 11,937 9 109 855 2 26,649 4,285 0 4,744 3 0 0 439 61 4 5,423 10,952 3,002 216 Total Output 97,795 120,594 14,642 47,473   Answer will be 4x4 matrix.

Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows. Max Department Product 1 Product 2 Product 3 s.t. A B с Department A Department B 1.50 Department C P₁, P2, P320 P1¹ 2.00 0.25 3.00 1.00 During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $23 for product 1, $27 for product 2, and $28 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let P; = units of product i produced, for i = 1, 2, 3.) 0.25 2.00 2.50 0.25 (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? (P₁, P₂, P3)-([ with profit $ (c) After evaluating the solution obtained in part (b), one of the production supervisors noted…