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23. The Radex Electronics Corporation is a medium-size electronics firm, one division of which specializes in made-to- order radar and ship-to-shore radio equipment. Radex has been awarded an Army contract to assemble and deliver a number of special radar units that are small enough and light enough to be carried on a man's back. Radex receives $500 for each radar unit and the delivery schedule is as follows: Shipping date Requirements Cumulative shipments 1 April 300 300 1 May 400 700 1 June 300 1000 The actual cumulative shipments cannot exceed this schedule, since the Army, in order to have time for effective testing before accepting all units, will refuse to accept any faster delivery. Further, it is permissible in the terms of the contract to ship the radar units late; however, a penalty cost of $50 is assessed for each radar unit that is shipped late. If this division of Radex produces faster than the given schedule, then it must purchase storage space in the company warehouse at $10 per assembled radar unit on hand on the first of the month (after the shipment is sent out). Production requirements are as follows: One radar unit requires 43 standard hours of assembly labor; one trained man (with more than one month's experience), working at 100% efficiency, produces 172 standard hours of output per month, regular time; one new man (with less than one month's experience), rated at 75% efficiency, produces 129 standard hours of output per month. The labor requirements are as follows: Employees are paid $5.00 per hour of regular time and $7.50 per hour of overtime; a maximum of 35 hours of overtime is allowed per month, but new men may not work overtime; each man on the payroll is guaranteed 172 regular-time hours (that is, $860 per month); at the end of the month, five percent of the labor force quits; hiring costs are $200 per man, and all hiring is done on the first of the month On 1 March, Radex begins work on the government contract with 90 trained men on the payroll, and new men can be hired immediately. On completion of the contract 1 June, Radex will begin work on a new contract requiring 200 trained men. Construct the coefficient matrix for a linear program to optimize the operations of this division of the Radex Electronics Corporation over the indicated time period. Briefly define the variables and explain the significance of the equations. (Suggestion: Set up the block of the coefficient matrix corresponding to the March decisions first, then indicate how additional blocks should be constructed.)
