Optimization Theory Applied Mathematics Laboratory assignments 3. (Based on (BHM77]) An important problem in production management is the allocation of a given production quantity (determined by an aggregate model or by subjective managerial inputs) among a group of items. For example, let us assume that we have decided to produce P = 8000 units of a given product line consisting of three individual items. The allocation of the total quantity among the three items will be decided by the following mathematical model: minimize c=Z= (1 + si) subject to -Qi =P where: Qi is the production quantity for item i in units), h; is inventory holding cost for item i in $ per month x unit), S is the setup cost for item i in $). d; is the demand for item i (in units per month), P is the total amount to be produced (in units). Write a procedure allowing you to solve this problem applying the method of multipliers and Newton's method with Armijo rule used to choose the stepsize used to solve the subproblems encountered. Apply it for the following values of the parameters: h, = 1, h2 = 13 = 2, S = 150, S2 190, $3 = 300, di = 15000, d, = 45000, dz = 40000. Optimization Theory Applied Mathematics Laboratory assignments 3. (Based on (BHM77]) An important problem in production management is the allocation of a given production quantity (determined by an aggregate model or by subjective managerial inputs) among a group of items. For example, let us assume that we have decided to produce P = 8000 units of a given product line consisting of three individual items. The allocation of the total quantity among the three items will be decided by the following mathematical model: minimize c=Z= (1 + si) subject to -Qi =P where: Qi is the production quantity for item i in units), h; is inventory holding cost for item i in $ per month x unit), S is the setup cost for item i in $). d; is the demand for item i (in units per month), P is the total amount to be produced (in units). Write a procedure allowing you to solve this problem applying the method of multipliers and Newton's method with Armijo rule used to choose the stepsize used to solve the subproblems encountered. Apply it for the following values of the parameters: h, = 1, h2 = 13 = 2, S = 150, S2 190, $3 = 300, di = 15000, d, = 45000, dz = 40000