Problem $3-31$

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on

two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir

capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only $0\mathrm{.}5\%$ of the capacitors provided by Lyshenko had to be

discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only $1\%$ unacceptable capacitors. Because Gulf Coast Electronics has

had no experience with Boston Components, it estimated Boston Components' defective rate to be $10\%.$ Gulf Coast would like to determine how many reservoir capacitors should be ordered

from each firm to obtain $75,000$ acceptable$-$quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that

the volume of reservoir capacitors awarded to Boston Components must be at least $10\%$ of the volume given to Able Controls. In addition, the total volume assigned to Boston Components,

Able Controls, and Lyshenko Industries should not exceed $30,000,50,700,$ and $50,000$ capacitors, respectively. Because of Gulf Coast's long$-$term relationship with Lyshenko Industries,

management also specified that at least $30,000$ capacitors should be ordered from Lyshenko. The cost per capacitor is $$2\mathrm{.}45$ for Boston Components, $$2\mathrm{.}50$ for Able Controls, and $$2\mathrm{.}75$ for

Lyshenko Industries.

a$.$ Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining $75,000$ acceptable$-$quality

reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank. If constant is $"1",$ it must be entered in the box.

Let $B=$ number of capacitors ordered from Boston Components

Let $A=$ number of capacitors ordered from Able Controls

Let $L=$ number of capacitors ordered from Lyshenko IndustriesProblem $3-31$

Gulf Coast Electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. For the past several years, Gulf Coast Electronics has relied on

two suppliers for its reservoir capacitors: Able Controls and Lyshenko Industries. A new firm, Boston Components, has inquired into the possibility of providing a portion of the reservoir

capacitors needed by Gulf Coast. The quality of products provided by Lyshenko Industries has been extremely high; in fact, only $0\mathrm{.}5\%$ of the capacitors provided by Lyshenko had to be

discarded because of quality problems. Able Controls has also had a high quality level historically, producing an average of only $1\%$ unacceptable capacitors. Because Gulf Coast Electronics has

had no experience with Boston Components, it estimated Boston Components' defective rate to be $10\%.$ Gulf Coast would like to determine how many reservoir capacitors should be ordered

from each firm to obtain $75,000$ acceptable$-$quality capacitors to use in its electronic devices. To ensure that Boston Components will receive some of the contract, management specified that

the volume of reservoir capacitors awarded to Boston Components must be at least $10\%$ of the volume given to Able Controls. In addition, the total volume assigned to Boston Components,

Able Controls, and Lyshenko Industries should not exceed $30,000,50,700,$ and $50,000$ capacitors, respectively. Because of Gulf Coast's long$-$term relationship with Lyshenko Industries,

management also specified that at least $30,000$ capacitors should be ordered from Lyshenko. The cost per capacitor is $$2\mathrm{.}45$ for Boston Components, $$2\mathrm{.}50$ for Able Controls, and $$2\mathrm{.}75$ for

Lyshenko Industries.

a$.$ Formulate and solve a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining $75,000$ acceptable$-$quality

reservoir capacitors. For subtractive or negative numbers use a minus sign even if there is a $+$ sign before the blank. If constant is $"1",$ it must be entered in the box.

Let $B=$ number of capacitors ordered from Boston Components

Let $A=$ number of