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A-manufactual-plans-to-build-two-types-of-tables-For-table-A-the-cost-of-material-is-20-000-bucks-the-number-of-man-hours-needed-to-complete-it-is-10-and-the-profit-is-15-000-bucks-Table-B-requ




Question Number 38051 by Rio Mike last updated on 21/Jun/18
A manufactual plans to build two  types of tables. For table A,the cost  of material is 20 000 bucks, the   number of man hours needed to   complete it is 10, and the profit   is 15 000 bucks. Table B requires  materials costing 12000 bucks,15  man hour of labour and makes  same profit as table A.    The total money avialable for materials  is 500 000 bucks and labour avialable  is 330 man hours.Find the maximum  profit that can be made and the number of each  type of table that should be made to produces  it.
$${A}\:{manufactual}\:{plans}\:{to}\:{build}\:{two} \\ $$$${types}\:{of}\:{tables}.\:{For}\:{table}\:{A},{the}\:{cost} \\ $$$${of}\:{material}\:{is}\:\mathrm{20}\:\mathrm{000}\:{bucks},\:{the}\: \\ $$$${number}\:{of}\:{man}\:{hours}\:{needed}\:{to}\: \\ $$$${complete}\:{it}\:{is}\:\mathrm{10},\:{and}\:{the}\:{profit}\: \\ $$$${is}\:\mathrm{15}\:\mathrm{000}\:{bucks}.\:{Table}\:{B}\:{requires} \\ $$$${materials}\:{costing}\:\mathrm{12000}\:{bucks},\mathrm{15} \\ $$$${man}\:{hour}\:{of}\:{labour}\:{and}\:{makes} \\ $$$${same}\:{profit}\:{as}\:{table}\:{A}. \\ $$$$\:\:{The}\:{total}\:{money}\:{avialable}\:{for}\:{materials} \\ $$$${is}\:\mathrm{500}\:\mathrm{000}\:{bucks}\:{and}\:{labour}\:{avialable} \\ $$$${is}\:\mathrm{330}\:{man}\:{hours}.{Find}\:{the}\:{maximum} \\ $$$${profit}\:{that}\:{can}\:{be}\:{made}\:{and}\:{the}\:{number}\:{of}\:{each} \\ $$$${type}\:{of}\:{table}\:{that}\:{should}\:{be}\:{made}\:{to}\:{produces} \\ $$$${it}. \\ $$

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