Can you solve (2.13) without a spreadsheet or technology. Just show the profit, constraints, and variable declaration please.

2.13. Alpha-Beta. Inc.. needs to schedule the weekly production of widgets and gadgers for the next 4 weeks. The production of widgets and gadgets requires machining a single raw material. Each widget requires 2 pounds of raw material and 24 minutes of machine time; each gadget requires 2.4 pounds of raw material and 18 minutes of trachine time. Each pound of raw material currentiy cosis $2.10, but the price is expected to rise $0.20 per pound each week. There is no storage area ayailabie for raw material and Alpha-Beta must purchase the raw material used in a given week during that week. The total machine time available during each week is 120 hours at: a cost of $18 per hour. In addition, 40 hours of overtime are available each week at a cost of $30 per hour. However, the cost of a machine-hour is expected to rise 10%6 during the last week. The projected weekly demands for widgets are 100. 120, 200. 150 units, and the weekly demands for Gadgets are 80.90. 115. 160 units. A maximum of 40 units of excess production can be stored from one week to the next at a cost of $3 per unit. Assuming that beginning inventory levels are zero, develop a linear programming model to determine the optimal production and inventory scheduies. 2.14. The preliminary layout of a communications network has been determined and is illustrated in the accompanying network diagram. The links of this network are depicted as branches, or ares between each node pair, and the cost of transmitting a single message unit is indicated beside each link. The nodes of the network (with the exception of nodes 1 and 5 , which are simply transmission and reception terminals) actually represent repeater stations (whose purposes are to receive, amplify, error check, and transmit any messages received, per second, at the station). Further