The cost to run Machine 1 for an hour is $2. During that hour, Machine 1 produce

Question

The cost to run Machine 1 for an hour is $2. During that hour, Machine 1 produces 240 bolts and 100 nuts. The cost to run Machine 2 for an hour is $2.40. During that hour, Machine 2 produces 160 bolts and 160 nuts. With a combined running time of no more than 30 hours, how long should each machine run to produce an order of at least 2080 bolts and nuts at the minimum operating cost?

Explanation / Answer

The cost to run machine 1 for an hour is $2. During that hour, Machine 1 produces 240 bolts and 100 nuts. ----------------------------------------------------------------- The cost to run machine 2 for an hour is $2.40. During that hour, Machine 2 produces 160 bolts and 160 nuts. ----------------------------------------------------------------- With a combined running time of no more that 30 hours, how long should each machine run to produce an order of at least 2080 bolts and 1520 nuts at the minimum operating cost? ---------------------------------- Let "x" be machine 1 running time: x >= 0 Let "y" be machine 2 running time: y >= 0 ------ Objective Function: Cost = 2x + 2.40y This is the function to be minimized ---------------------- Equations: time: x + y = 7 bolts: 240x + 160y >=2080 nuts:: 100x + 160y >- 1520 ------------------------------- Solve equations/inequlities for y and graph. --- I guess you know the rest of the procedure

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