Set up the mathematical formulation of linear programming problem for the following optimization problems. Solve them using Excel Solver a. Failsafe Electronics Corporation primarily manufactures four highly technical products, which it supplies to aerospace firms that hold NASA contracts. Each of the products must pass through the following departments before they are shipped: wiring, drilling, assembly and inspection. The time requirements in each department (in hours) for each unit produced and its corresponding profit value are summarized in this table: PRODUCT WIRING DRILLING ASSEMBLY INSPECTION UNIT PROFIT XJ201 XM897 TR29 BR788 1.5 1.5 1.0 DEPARTMENT 3 1 2 3 CAPACITY (IN HOURS) 24 1 2 1,500 2,350 2,600 1,200 1.0 .5 .5 The production time available in each department each month and the minimum monthly production requirement to fulfill contracts are as follows: MINIMUM DEPARTMENT PRODUCT PRODUCTION LEVEL Wiring XJ201 Drilling XM897 Assembly TR29 Inspection BR788 Find the number of units of each product that needs to be produced in order to maximize profit. $9 $12 $15 $11 150 100 300 400