A hospital is planning an $8 million addition to its existing facility. The arch

Question

A hospital is planning an $8 million addition to its existing facility. The architect has been asked to consider the following design paremeters: (1) There should be at least 10 and no more than 20 intensive care unit (ICU) rooms: (2) there should be at least 10 and no more than 20 cardiac care unit (CCU); (3) there should be no more than 50 double rooms; (4) there should be at least 35 single rooms; and (5) all patient rooms should fit in the alocated 40,000 square foot space (not including hallways) The following table summarizes the relevant room data:

Single Double ICU CCU

Cost per room $45000 $54000 $110000 $104000

Square feet required 300 360 320 340

Profit per room per $21000 $28000 $48000 $41000

month

Explanation / Answer

This is an LPP problem : linear programming problem

here let us say, x1 = no of CCU

x2 = no of single rooms

x3 = no of double rooms

x4 = no of ICU

we need to try to maximize the profit per month i.e " 41000 * x1 + 21,000 * x2 + 28000 * x3 + 48000 *x4 "

with the conditions that total cost = $8 million
==> 104000*x1 + 45000*x2 + 54000*x3 + 110000*x4 < 8,000,000 (8 million)

==> 104*x1 + 45*x2 + 54*x3 + 110*x4 = 8,000
& 10 < x1 < 20 ;

& 10 < x4 < 20 ;

& x3 <50 (no more than 50 double rooms)

& x2 > 35 (at least single rooms)

& 340*x1 + 300*x2 + 360*x3 + 320*x4 < 40,000 ( allocated space)

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